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Chapter 12 A1 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Anticipation Guide and Lesson 12-1)
Cha
pter
12
5G
lenc
oe A
lgeb
ra 2
Lesson 12-1
12-1
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Th
e C
ou
nti
ng
Pri
nci
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
2-1
in y
our
text
boo
k.
Ass
um
e th
at a
ll F
lori
da l
icen
se p
late
s h
ave
thre
e le
tter
s fo
llow
ed b
y th
ree
digi
ts,a
nd
that
ther
e ar
e n
o ru
les
agai
nst
usi
ng
the
sam
e le
tter
or
nu
mbe
r m
ore
than
on
ce.H
ow m
any
choi
ces
are
ther
e fo
r ea
ch l
ette
r? f
or e
ach
dig
it?
26;
10
Rea
d t
he
Less
on
1.S
ham
im i
s si
gnin
g u
p fo
r h
er c
lass
es.M
ost
of h
er c
lass
es a
re r
equ
ired
,bu
t sh
e h
as t
wo
elec
tive
s.F
or h
er a
rts
clas
s,sh
e ca
n c
hos
e be
twee
n A
rt,B
and,
Ch
oru
s,or
Dra
ma.
For
her
lan
guag
e cl
ass,
she
can
ch
oose
bet
wee
n F
ren
ch,G
erm
an,a
nd
Spa
nis
h.
a.T
o or
gan
ize
her
ch
oice
s,S
ham
im d
ecid
es t
o m
ake
a tr
ee d
iagr
am.L
et A
,B,C
,an
d D
repr
esen
t A
rt,B
and,
Ch
oru
s,an
d D
ram
a,an
d F,
G,a
nd
S r
epre
sen
t F
ren
ch,G
erm
an,
and
Spa
nis
h.C
ompl
ete
the
foll
owin
g di
agra
m.
b.
How
cou
ld S
ham
im h
ave
foun
d th
e nu
mbe
r of
pos
sibl
e co
mbi
nati
ons
wit
hout
mak
ing
atr
ee d
iagr
am?
Sam
ple
an
swer
:Mu
ltip
ly t
he
nu
mb
er o
f ch
oic
es f
or
her
art
scl
ass
by t
he
nu
mb
er o
f ch
oic
es f
or
her
lan
gu
age
clas
s:4
�3
�12
.
2.A
jar
con
tain
s 6
red
mar
bles
,4 b
lue
mar
bles
,an
d 3
yell
ow m
arbl
es.I
ndi
cate
wh
eth
er t
he
even
ts d
escr
ibed
are
dep
end
ent
or i
nd
epen
den
t.
a.A
mar
ble
is d
raw
n o
ut
of t
he
jar
and
is n
ot r
epla
ced.
A s
econ
d m
arbl
e is
dra
wn
.d
epen
den
t
b.
A m
arbl
e is
dra
wn
ou
t of
th
e ja
r an
d is
pu
t ba
ck i
n.T
he
jar
is s
hak
en.A
sec
ond
mar
ble
is d
raw
n.
ind
epen
den
t
Rem
emb
er W
hat
Yo
u L
earn
ed
3.O
ne
defi
nit
ion
of
ind
epen
den
tis
“n
ot d
eter
min
ed o
r in
flu
ence
d by
som
eon
e or
som
eth
ing
else
.”H
ow c
an t
his
def
init
ion
hel
p yo
u r
emem
ber
the
diff
eren
ce b
etw
een
in
dep
end
ent
and
dep
end
ent
even
ts?
Sam
ple
an
swer
:If
th
e o
utc
om
e o
f o
ne
even
t d
oes
no
taf
fect
or
infl
uen
ce t
he
ou
tco
me
of
ano
ther
,th
e ev
ents
are
ind
epen
den
t.If
th
e o
utc
om
e o
f o
ne
even
t d
oes
affe
ct o
r in
flu
ence
th
e o
utc
om
e o
fan
oth
er,t
he
even
ts a
re d
epen
den
t.
FGA
S
AF
AG
AS
FGB
S
BF
BG
BS
FGC
S
CF
CG
CS
FGD
S
DF
DG
DS
Cha
pter
12
3G
lenc
oe A
lgeb
ra 2
12
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Ant
icip
atio
n G
uide
Pro
bab
ility
an
d S
tati
stic
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Bef
ore
you
beg
in C
ha
pte
r 12
•R
ead
each
sta
tem
ent.
•D
ecid
e w
het
her
you
Agr
ee (
A)
or D
isag
ree
(D)
wit
h t
he
stat
emen
t.
•W
rite
A o
r D
in
th
e fi
rst
colu
mn
OR
if
you
are
not
su
re w
het
her
you
agr
ee o
r di
sagr
ee,
wri
te N
S(N
ot S
ure
).
Aft
er y
ou c
omp
lete
Ch
ap
ter
12
•R
erea
d ea
ch s
tate
men
t an
d co
mpl
ete
the
last
col
um
n b
y en
teri
ng
an A
or
a D
.
•D
id a
ny
of y
our
opin
ion
s ab
out
the
stat
emen
ts c
han
ge f
rom
th
e fi
rst
colu
mn
?
•F
or t
hos
e st
atem
ents
th
at y
ou m
ark
wit
h a
D,u
se a
pie
ce o
f pa
per
to w
rite
an
exa
mpl
e of
wh
y yo
u d
isag
ree.
Step
1
ST
EP
1S
TE
P 2
A,D
,or
NS
Sta
tem
ent
A o
r D
1.A
sam
ple
spac
e is
a p
arti
al l
ist
of p
ossi
ble
outc
omes
of
an
expe
rim
ent.
D
2.T
wo
even
ts a
re c
alle
d in
depe
nde
nt
if c
hoo
sin
g on
e do
es n
ot
affe
ct c
hoo
sin
g th
e ot
her
.A
3.A
ccor
din
g to
th
e F
un
dam
enta
l C
oun
tin
g P
rin
cipl
e,if
on
e ev
ent
can
occ
ur
in 6
way
s an
d an
oth
er e
ven
t ca
n o
ccu
r in
D
3 w
ays,
then
th
e ev
ents
tog
eth
er c
an o
ccu
r in
6 �
3 or
9 w
ays.
4.S
ince
ord
er i
s n
ot i
mpo
rtan
t in
a c
ombi
nat
ion
,an
ou
tcom
e ab
is t
he
sam
e as
an
ou
tcom
e ba
.A
5.T
he
odds
of
an e
ven
t oc
curr
ing
can
be
expr
esse
d as
a r
atio
of
th
e n
um
ber
of s
ucc
esse
s to
th
e to
tal
nu
mbe
r of
ou
tcom
es.
D
6.If
two
even
tsar
ede
pen
den
t,th
enth
epr
obab
ilit
yof
both
even
ts
occu
rrin
g is
th
e pr
odu
ct o
f th
e pr
obab
ilit
ies
of e
ach
eve
nt.
D
7.T
wo
even
ts a
re m
utu
ally
exc
lusi
veif
th
ey c
ann
ot o
ccu
r at
th
e sa
me
tim
e.A
8.If
a s
et o
f da
ta c
onta
ins
outl
iers
,th
e m
edia
n w
ould
be
a go
od
choi
ce t
o re
pres
ent
the
set.
A
9.M
easu
res
of v
aria
tion
are
th
e di
ffer
ence
s be
twee
n c
onse
cuti
ve
valu
es i
n t
he
set.
D
10.
Th
e cu
rve
repr
esen
tin
g a
nor
mal
dis
trib
uti
on i
s sy
mm
etri
c.A
11.
Th
e B
inom
ial T
heo
rem
can
be
use
d to
fin
d pr
obab
ilit
ies
only
w
hen
th
ere
are
two
poss
ible
ou
tcom
es.
A
12.
Ask
ing
peop
le i
n a
mu
sic
stor
e h
ow m
any
hou
rs t
hey
spe
nd
list
enin
g to
mu
sic
to d
eter
min
e h
ow m
any
hou
rs p
eopl
e in
th
e D
city
lis
ten
to
mu
sic
is a
n e
xam
ple
of a
n u
nbi
ased
su
rvey
.
Step
2
Chapter Resources
Chapter 12 A2 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 12-1)
Cha
pter
12
7G
lenc
oe A
lgeb
ra 2
Lesson 12-1
12-1
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Th
e C
ou
nti
ng
Pri
nci
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Dep
end
ent
Even
tsIf
th
e ou
tcom
e of
an
eve
nt
doe
saf
fect
th
e ou
tcom
e of
an
oth
er e
ven
t,th
e tw
o ev
ents
are
sai
d to
be
dep
end
ent.
The
Fun
dam
enta
l C
ount
ing
Pri
ncip
le s
till
app
lies
.
ENTE
RTA
INM
ENT
Th
e gu
ests
at
a sl
eep
over
bro
ugh
t 8
vid
eos.
Th
eyd
ecid
ed t
hey
wou
ld o
nly
wat
ch 3
vid
eos.
How
man
y or
der
s of
3 d
iffe
ren
t vi
deo
sar
e p
ossi
ble
?A
fter
th
e gr
oup
choo
ses
to w
atch
a v
ideo
,th
ey w
ill
not
ch
oose
to
wat
ch i
t ag
ain
,so
the
choi
ces
of v
ideo
s ar
e de
pen
den
t ev
ents
.
Th
ere
are
8 ch
oice
s fo
r th
e fi
rst
vide
o.T
hat
lea
ves
7 ch
oice
s fo
r th
e se
con
d.A
fter
th
ey c
hoo
seth
e fi
rst
2 vi
deos
,th
ere
are
6 re
mai
nin
g ch
oice
s.T
hu
s,by
th
e F
un
dam
enta
l C
oun
tin
gP
rin
cipl
e,th
ere
are
8 �
7 �
6 or
336
ord
ers
of 3
dif
fere
nt
vide
os.
Sol
ve e
ach
pro
ble
m.
1.T
hre
e st
ude
nts
are
sch
edu
led
to g
ive
oral
rep
orts
on
Mon
day.
In h
ow m
any
way
s ca
nth
eir
pres
enta
tion
s be
ord
ered
?6
2.In
how
man
y w
ays
can
th
e fi
rst
five
let
ters
of
the
alph
abet
be
arra
nge
d if
eac
h l
ette
r is
use
d on
ly o
nce
?12
0
3.In
how
man
y di
ffer
ent
way
s ca
n 4
dif
fere
nt
book
s be
arr
ange
d on
th
e sh
elf?
24
4.H
ow m
any
lice
nse
pla
tes
con
sist
ing
of t
hre
e le
tter
s fo
llow
ed b
y th
ree
nu
mbe
rs a
repo
ssib
le w
hen
no
repe
titi
on i
s al
low
ed?
11,2
32,0
00
5.S
ixte
en t
eam
s ar
e co
mpe
tin
g in
a s
occe
r m
atch
.Gol
d,si
lver
,an
d br
onze
med
als
wil
l be
awar
ded
to t
he t
op t
hree
fin
ishe
rs.I
n ho
w m
any
way
s ca
n th
e m
edal
s be
aw
arde
d?33
60
6.In
a w
ord-
buil
din
g ga
me
each
pla
yer
pick
s 7
lett
er t
iles
.If
Juli
o’s
lett
ers
are
all
diff
eren
t,h
ow m
any
3-le
tter
com
bin
atio
ns
can
he
mak
e ou
t of
his
7 l
ette
rs?
210
7.T
he e
dito
r ha
s ac
cept
ed 6
art
icle
s fo
r th
e ne
wsl
ette
r.In
how
man
y w
ays
can
the
6 ar
ticl
esbe
ord
ered
?72
0
8.T
her
e ar
e 10
on
e-h
our
wor
ksh
ops
sch
edu
led
for
the
open
hou
se a
t th
e gr
een
hou
se.
Th
ere
is o
nly
on
e co
nfe
ren
ce r
oom
ava
ilab
le.I
n h
ow m
any
way
s ca
n t
he
wor
ksh
ops
beor
dere
d?3,
628,
800
9.T
he
top
5 ru
nn
ers
at t
he
cros
s-co
un
try
mee
t w
ill
rece
ive
trop
hie
s.If
th
ere
are
22 r
un
ner
sin
th
e ra
ce,i
n h
ow m
any
way
s ca
n t
he
trop
hie
s be
aw
arde
d?3,
160,
080
Exam
ple
Exer
cise
s
Cha
pter
12
6G
lenc
oe A
lgeb
ra 2
12-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Th
e C
ou
nti
ng
Pri
nci
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Ind
epen
den
t Ev
ents
If t
he
outc
ome
of o
ne
even
t do
es n
ot a
ffec
t th
e ou
tcom
e of
anot
her
eve
nt
and
vice
ver
sa,t
he
even
ts a
re c
alle
d in
dep
end
ent
even
ts.
Fu
nd
amen
tal
If ev
ent
Mca
n oc
cur
in m
way
s an
d is
follo
wed
by
even
t N
that
can
occ
ur in
nw
ays,
C
ou
nti
ng
Pri
nci
ple
then
the
eve
nt M
follo
wed
by
the
even
t N
can
occu
r in
m�
nw
ays.
FOO
DF
or t
he
Bre
akfa
st S
pec
ial
at t
he
Cou
ntr
y P
antr
y,cu
stom
ers
can
ch
oose
th
eir
eggs
scr
amb
led
,fri
ed,o
r p
oach
ed,w
hol
e w
hea
t or
wh
ite
toas
t,an
d e
ith
er o
ran
ge,a
pp
le,t
omat
o,or
gra
pef
ruit
ju
ice.
How
man
y d
iffe
ren
tB
reak
fast
Sp
ecia
ls c
an a
cu
stom
er o
rder
?A
cu
stom
er’s
ch
oice
of
eggs
doe
s n
ot a
ffec
t h
is o
r h
er c
hoi
ce o
f to
ast
or ju
ice,
so t
he
even
tsar
e in
depe
nde
nt.
Th
ere
are
3 w
ays
to c
hoo
se e
ggs,
2 w
ays
to c
hoo
se t
oast
,an
d 4
way
s to
choo
se ju
ice.
By
the
Fu
nda
men
tal
Cou
nti
ng
Pri
nci
ple,
ther
e ar
e 3
�2
�4
or 2
4 w
ays
toch
oose
th
e B
reak
fast
Spe
cial
.
Sol
ve e
ach
pro
ble
m.
1.T
he
Pal
ace
of P
izza
off
ers
smal
l,m
ediu
m,o
r la
rge
pizz
as w
ith
14
diff
eren
t to
ppin
gsav
aila
ble.
How
man
y di
ffer
ent
one-
topp
ing
pizz
as d
o th
ey s
erve
?42
2.T
he
lett
ers
A,B
,C,a
nd
D a
re u
sed
to f
orm
fou
r-le
tter
pas
swor
ds f
or e
nte
rin
g a
com
pute
rfi
le.H
ow m
any
pass
wor
ds a
re p
ossi
ble
if l
ette
rs c
an b
e re
peat
ed?
256
3.A
res
tau
ran
t se
rves
5 m
ain
dis
hes
,3 s
alad
s,an
d 4
dess
erts
.How
man
y di
ffer
ent
mea
lsco
uld
be
orde
red
if e
ach
has
a m
ain
dis
h,a
sal
ad,a
nd
a de
sser
t?60
4.M
aris
sa b
rou
ght
8 T-
shir
ts a
nd
6 pa
irs
of s
hor
ts t
o su
mm
er c
amp.
How
man
y di
ffer
ent
outf
its
con
sist
ing
of a
T-s
hir
t an
d a
pair
of
shor
ts d
oes
she
hav
e?48
5.T
her
e ar
e 6
diff
eren
t pa
ckag
es a
vail
able
for
sch
ool
pict
ure
s.T
he
stu
dio
offe
rs 5
dif
fere
nt
back
grou
nds
an
d 2
diff
eren
t fi
nis
hes
.How
man
y di
ffer
ent
opti
ons
are
avai
labl
e?60
6.H
ow m
any
5-di
git
even
nu
mbe
rs c
an b
e fo
rmed
usi
ng
the
digi
ts 4
,6,7
,2,8
if
digi
ts c
anbe
rep
eate
d?25
00
7.H
ow m
any
lice
nse
pla
te n
um
bers
con
sist
ing
of t
hre
e le
tter
s fo
llow
ed b
y th
ree
nu
mbe
rsar
e po
ssib
le w
hen
rep
etit
ion
is
allo
wed
?17
,576
,000
8.H
ow m
any
4-di
git
posi
tive
eve
n i
nte
gers
are
th
ere?
4500
Exam
ple
Exer
cise
s
Chapter 12 A3 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 12-1)
Cha
pter
12
9G
lenc
oe A
lgeb
ra 2
Lesson 12-1
12-1
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Prac
tice
Th
e C
ou
nti
ng
Pri
nci
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Sta
te w
het
her
th
e ev
ents
are
in
dep
end
ent
or d
epen
den
t.
1.ch
oosi
ng
an i
ce c
ream
fla
vor
and
choo
sin
g a
topp
ing
for
the
ice
crea
min
dep
end
ent
2.ch
oosi
ng
an o
ffen
sive
pla
yer
of t
he
gam
e an
d a
defe
nsi
ve p
laye
r of
th
e ga
me
in a
prof
essi
onal
foo
tbal
l ga
me
ind
epen
den
t
3.F
rom
15
entr
ies
in a
n a
rt c
onte
st,a
cam
p co
un
selo
r ch
oose
s fi
rst,
seco
nd,
and
thir
d pl
ace
win
ner
s.d
epen
den
t
4.Ji
llia
n i
s se
lect
ing
two
mor
e co
urs
es f
or h
er b
lock
sch
edu
le n
ext
sem
este
r.S
he
mu
stse
lect
on
e of
th
ree
mor
nin
g h
isto
ry c
lass
es a
nd
one
of t
wo
afte
rnoo
n m
ath
cla
sses
.in
dep
end
ent
Sol
ve e
ach
pro
ble
m.
5.A
bri
efca
se l
ock
has
3 r
otat
ing
cyli
nde
rs,e
ach
con
tain
ing
10 d
igit
s.H
ow m
any
nu
mer
ical
code
s ar
e po
ssib
le?
1000
6.A
gol
f cl
ub
man
ufa
ctu
rer
mak
es i
ron
s w
ith
7 d
iffe
ren
t sh
aft
len
gth
s,3
diff
eren
t gr
ips,
5di
ffer
ent
lies
,an
d 2
diff
eren
t cl
ub
hea
d m
ater
ials
.How
man
y di
ffer
ent
com
bin
atio
ns
are
offe
red?
210
7.T
her
e ar
e fi
ve d
iffe
ren
t ro
ute
s th
at a
com
mu
ter
can
tak
e fr
om h
er h
ome
to t
he
offi
ce.I
nh
ow m
any
way
s ca
n s
he
mak
e a
rou
nd
trip
if
she
use
s a
diff
eren
t ro
ute
com
ing
than
goin
g?20
8.In
how
man
y w
ays
can
th
e fo
ur
call
let
ters
of
a ra
dio
stat
ion
be
arra
nge
d if
th
e fi
rst
lett
er m
ust
be
W o
r K
an
d n
o le
tter
s re
peat
?27
,600
9.H
ow m
any
7-di
git
phon
e n
um
bers
can
be
form
ed i
f th
e fi
rst
digi
t ca
nn
ot b
e 0
or 1
,an
dan
y di
git
can
be
repe
ated
?8,
000,
000
10.H
ow m
any
7-di
git
phon
e n
um
bers
can
be
form
ed i
f th
e fi
rst
digi
t ca
nn
ot b
e 0,
and
any
digi
t ca
n b
e re
peat
ed?
9,00
0,00
0
11.H
ow m
any
7-di
git
phon
e n
um
bers
can
be
form
ed i
f th
e fi
rst
digi
t ca
nn
ot b
e 0
or 1
,an
dn
o di
git
can
be
repe
ated
?48
3,84
0
12.H
ow m
any
7-di
git
phon
e n
um
bers
can
be
form
ed i
f th
e fi
rst
digi
t ca
nn
ot b
e 0,
and
no
digi
t ca
n b
e re
peat
ed?
544,
320
13.H
ow m
any
6-ch
arac
ter
pass
wor
ds c
an b
e fo
rmed
if
the
firs
t ch
arac
ter
is a
dig
it a
nd
the
rem
ain
ing
5 ch
arac
ters
are
let
ters
th
at c
an b
e re
peat
ed?
118,
813,
760
14.H
ow m
any
6-ch
arac
ter
pass
wor
ds c
an b
e fo
rmed
if
the
firs
t an
d la
st c
har
acte
rs a
redi
gits
an
d th
e re
mai
nin
g ch
arac
ters
are
let
ters
? A
ssu
me
that
an
y ch
arac
ter
can
be
repe
ated
.45
,697
,600
Cha
pter
12
8G
lenc
oe A
lgeb
ra 2
12-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceT
he
Co
un
tin
g P
rin
cip
le
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Sta
te w
het
her
th
e ev
ents
are
in
dep
end
ent
or d
epen
den
t.
1.fi
nis
hin
g in
fir
st,s
econ
d,or
th
ird
plac
e in
a t
en-p
erso
n r
ace
dep
end
ent
2.ch
oosi
ng
a pi
zza
size
an
d a
topp
ing
for
the
pizz
ain
dep
end
ent
3.S
even
ty-f
ive
raff
le t
icke
ts a
re p
lace
d in
a ja
r.T
hre
e ti
cket
s ar
e th
en s
elec
ted,
one
afte
rth
e ot
her
,wit
hou
t re
plac
ing
a ti
cket
aft
er i
t is
ch
osen
.d
epen
den
t
4.T
he
232
mem
bers
of
the
fres
hm
an c
lass
all
vot
e by
sec
ret
ball
ot f
or t
he
clas
sre
pres
enta
tive
to
the
Stu
den
t S
enat
e.in
dep
end
ent
Sol
ve e
ach
pro
ble
m.
5.A
su
rvey
ing
firm
pla
ns
to b
uy
a co
lor
prin
ter
for
prin
tin
g it
s m
aps.
It h
as n
arro
wed
its
choi
ce t
o on
e of
th
ree
mod
els.
Eac
h o
f th
e m
odel
s is
ava
ilab
le w
ith
eit
her
32
meg
abyt
esof
ran
dom
acc
ess
mem
ory
(RA
M),
64 m
egab
ytes
of
RA
M,o
r 12
8 m
egab
ytes
of
RA
M.
Fro
m h
ow m
any
com
bin
atio
ns
of m
odel
s an
d R
AM
doe
s th
e fi
rm h
ave
to c
hoo
se?
9
6.H
ow m
any
arra
nge
men
ts o
f th
ree
lett
ers
can
be
form
ed f
rom
th
e le
tter
s of
th
e w
ord
MA
TH
if a
ny
lett
er w
ill
not
be
use
d m
ore
than
on
ce?
24
7.A
llan
is
play
ing
the
role
of
Oli
ver
in h
is s
choo
l’s p
rodu
ctio
n o
f O
live
r T
wis
t.T
he
war
drob
e cr
ew h
as p
rese
nte
d A
llan
wit
h 5
pai
rs o
f pa
nts
an
d 4
shir
ts t
hat
he
can
wea
r.F
rom
how
man
y po
ssib
le c
ostu
mes
con
sist
ing
of a
pai
r of
pan
ts a
nd
a sh
irt
does
All
anh
ave
to c
hoo
se?
20
8.T
he 1
0-m
embe
r st
eeri
ng c
omm
itte
e th
at i
s pr
epar
ing
a st
udy
of t
he p
ubli
c tr
ansp
orta
tion
nee
ds o
f it
s to
wn
wil
l se
lect
a c
hai
rper
son
,vic
e-ch
airp
erso
n,a
nd
secr
etar
y fr
om t
he
com
mit
tee.
No
pers
on c
an s
erve
in
mor
e th
an o
ne
posi
tion
.In
how
man
y w
ays
can
th
eth
ree
posi
tion
s be
fil
led?
720
9.Je
anin
e h
as d
ecid
ed t
o bu
y a
pick
up
tru
ck.H
er c
hoi
ces
incl
ude
eit
her
a V
-6 e
ngi
ne
or a
V-8
en
gin
e,a
stan
dard
cab
or
an e
xten
ded
cab,
and
2-w
hee
l dr
ive
or 4
-wh
eel
driv
e.H
owm
any
poss
ible
mod
els
does
sh
e h
ave
to c
hoo
se f
rom
?8
10.A
mai
l-or
der
com
pan
y th
at s
ells
gar
den
ing
tool
s of
fers
rak
es i
n t
wo
diff
eren
t le
ngt
hs.
Cu
stom
ers
can
als
o ch
oose
eit
her
a w
oode
n,p
last
ic,o
r fi
berg
lass
han
dle
for
the
rake
.H
ow m
any
diff
eren
t ki
nds
of
rake
s ca
n a
cu
stom
er b
uy?
6
11.A
Mex
ican
res
tau
ran
t of
fers
ch
icke
n,b
eef,
or v
eget
aria
n f
ajit
as w
rapp
ed w
ith
eit
her
cor
nor
flo
ur
tort
illa
s an
d to
pped
wit
h e
ith
er m
ild,
med
ium
,or
hot
sal
sa.H
ow m
any
diff
eren
tch
oice
s of
faj
itas
doe
s a
cust
omer
hav
e?18
Chapter 12 A4 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 12-1)
Cha
pter
12
11G
lenc
oe A
lgeb
ra 2
Lesson 12-1
12-1
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Tree
Dia
gra
ms
and
th
e P
ow
er R
ule
If y
ou f
lip
a co
in o
nce
,th
ere
are
two
poss
ible
ou
tcom
es:h
eads
sh
owin
g (H
) or
tai
ls s
how
ing
(T).
Th
e tr
ee d
iagr
am t
o th
e ri
ght
show
s th
e fo
ur
(22 )
poss
ible
ou
tcom
es i
f yo
u f
lip
a co
in t
wic
e.
Flip
2
H T H T
Flip
1
H T
Ou
tco
mes
HH
HT
TH TT
star
t
Dra
w a
tre
e d
iagr
am t
osh
ow a
ll t
he
pos
sib
le o
utc
omes
for
fli
pp
ing
a co
in t
hre
e ti
mes
.Lis
t th
e ou
tcom
es.
Th
ere
are
eigh
t (2
3 ) p
ossi
ble
outc
omes
.Wit
hea
ch e
xtra
fli
p,th
e n
um
ber
of o
utc
omes
do
ubl
es.W
ith
4 f
lips
,th
ere
wou
ld b
e si
xtee
n(2
4 ) o
utc
omes
.
Flip
2
H T H T
Flip
1
H T
Flip
3
H T H T H T H T
Ou
tco
mes
HH
HH
HT
HT
HH
TT
TH
HT
HT
TT
HT
TT
star
t
In a
cu
p t
her
e ar
e a
red
,a b
lue,
and
a y
ello
w m
arb
le.H
owm
any
pos
sib
le o
utc
omes
are
th
ere
ifyo
u d
raw
on
e m
arb
le a
t ra
nd
om,
rep
lace
it,
and
th
en d
raw
an
oth
er?
Th
ere
are
nin
e (3
2 ) p
ossi
ble
outc
omes
.
Dra
w 2
R B Y R B Y R B Y
Ou
tco
mes
RR
RB
RY
BR
BB
BY
YR
YB
YY
Dra
w 1
R B Y
star
t
Th
e P
ower
Ru
le f
or t
he
nu
mbe
r of
ou
tcom
es s
tate
s th
at i
f an
exp
erim
ent
isre
peat
ed n
tim
es,a
nd
if t
her
e ar
e b
poss
ible
ou
tcom
es e
ach
tim
e,th
ere
are
bnto
tal
poss
ible
ou
tcom
es.
Fin
d t
he
tota
l n
um
ber
of
pos
sib
le o
utc
omes
for
eac
h e
xper
imen
t.U
setr
ee d
iagr
ams
to h
elp
you
.
1.fl
ippi
ng
a co
in 5
tim
es25
2.do
ing
the
mar
ble
expe
rim
ent
6 ti
mes
36
3.fl
ippi
ng
a co
in 8
tim
es28
4.ro
llin
g a
6-si
ded
die
2 ti
mes
62
5.ro
llin
g a
6-si
ded
die
3 ti
mes
636.
roll
ing
a 4-
side
d di
e 2
tim
es42
7.ro
llin
g a
4-si
ded
die
3 ti
mes
438.
roll
ing
a 12
-sid
ed d
ie 2
tim
es12
2
Exam
ple
1Ex
amp
le 2
Cha
pter
12
10G
lenc
oe A
lgeb
ra 2
12-1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Th
e C
ou
nti
ng
Pri
nci
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1.C
AN
DY
Am
y,B
ruce
,an
d C
arol
can
choo
se o
ne
piec
e of
can
dy f
rom
eit
her
a
wh
ite
or b
lack
bag
.Th
e w
hit
e ba
gco
nta
ins
vari
ous
choc
olat
es.T
he
blac
kba
g co
nta
ins
smal
l ba
gs o
f je
lly
bean
s.A
my
pick
s fr
om t
he
wh
ite
bag,
and
Bru
ce a
nd
Car
ol b
oth
pic
k fr
om t
he
blac
k ba
g.D
escr
ibe
wh
eth
er e
ach
of
the
pick
s is
rel
ated
as
depe
nde
nt
orin
depe
nde
nt
even
ts.
Am
y’s
pic
k is
ind
epen
den
t o
fea
ch o
f B
ruce
an
d C
aro
l’s p
icks
;B
ruce
an
d C
aro
l’s p
icks
are
exam
ple
s o
f d
epen
den
t ev
ents
.
2.PH
OTO
SM
orga
n h
as t
hre
e pi
ctu
res
that
sh
e w
ould
lik
e to
dis
play
sid
e by
sid
e.
In h
ow m
any
diff
eren
t w
ays
can
th
epi
ctu
res
be d
ispl
ayed
?6
3.C
OM
BIN
ATI
ON
LO
CK
SE
ric
use
s a
com
bin
atio
n l
ock
for
his
loc
ker.
Th
e lo
cku
ses
a th
ree
nu
mbe
r se
cret
cod
e.E
ach
nu
mbe
r ra
nge
s fr
om 1
to
35,i
ncl
usi
ve.
How
man
y di
ffer
ent
com
bin
atio
ns
are
poss
ible
wit
h E
ric’
s lo
ck?
42,8
75
4.TR
UE
OR
FA
LSE
Fait
h i
s pr
epar
ing
atr
ue
or f
alse
qu
iz f
or h
er b
iolo
gy c
lass
.H
ow m
any
diff
eren
t an
swer
key
s ca
nth
ere
be f
or a
10
ques
tion
tru
e or
fal
sequ
iz?
1024
WEB
SITE
SF
or E
xerc
ises
5-8
,use
th
efo
llow
ing
info
rmat
ion
.
Gre
g is
reg
iste
rin
g to
use
a w
ebsi
te.
Th
e w
ebsi
te r
equ
ires
him
to
choo
se a
n
8-ch
arac
ter
alph
anu
mer
ic p
assw
ord
that
is
not
cas
e-se
nsi
tive
.In
oth
er w
ords
,for
each
ch
arac
ter,
he
can
ch
oose
on
e of
th
e 26
let
ters
A t
hro
ugh
Z o
r on
e of
th
e 10
digi
ts 0
th
rou
gh 9
.
5.H
ow m
any
diff
eren
t pa
ssw
ords
are
poss
ible
?2,
821,
109,
907,
456
6.G
reg
deci
des
to u
se a
pas
swor
d th
at d
oes
not
con
tain
an
y re
peat
edch
arac
ters
.How
man
y di
ffer
ent
pass
wor
ds a
re p
ossi
ble
wit
h t
his
con
stra
int?
1,22
0,09
6,90
8,80
0
7.S
upp
ose
Gre
g ch
oose
s to
use
on
ly l
ette
rsw
ith
pos
sibl
e re
peat
s.H
ow m
any
diff
eren
t pa
ssw
ords
wou
ld b
e po
ssib
le?
208,
827,
064,
576
8.If
Gre
g’s
pass
wor
d be
gin
s w
ith
his
fir
stn
ame
and
ends
wit
h h
is b
irth
mon
than
d da
te,h
ow m
any
poss
ibil
itie
s w
ould
nee
d to
be
chec
ked
to f
ind
his
pas
swor
d?37
2
Chapter 12 A5 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 12-2)
Cha
pter
12
13G
lenc
oe A
lgeb
ra 2
Lesson 12-2
12-2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Per
mu
tati
on
s an
d C
om
bin
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Perm
uta
tio
ns
Wh
en a
gro
up
of o
bjec
ts o
r pe
ople
are
arr
ange
d in
a c
erta
in o
rder
,th
ear
ran
gem
ent
is c
alle
d a
per
mu
tati
on.
Per
mu
tati
on
sT
he n
umbe
r of
per
mut
atio
ns o
f ndi
stin
ct o
bjec
ts ta
ken
rat
a ti
me
is g
iven
by
P(n
, r)
�.
Per
mu
tati
on
s w
ith
Rep
etit
ion
sT
he n
umbe
r of
per
mut
atio
ns o
f n
obje
cts
of w
hich
par
e al
ike
and
qar
e al
ike
is
.
Th
e ru
le f
or p
erm
uta
tion
s w
ith
rep
etit
ion
s ca
n b
e ex
ten
ded
to a
ny
nu
mbe
r of
obj
ects
th
atar
e re
peat
ed.
Fro
m a
lis
t of
20
boo
ks,
each
stu
den
t m
ust
ch
oose
4 b
ook
s fo
r b
ook
rep
orts
.Th
e fi
rst
rep
ort
is a
tra
dit
ion
al b
ook
rep
ort,
the
seco
nd
a p
oste
r,th
e th
ird
a n
ewsp
aper
in
terv
iew
wit
h o
ne
of t
he
char
acte
rs,a
nd
th
e fo
urt
h a
tim
elin
e of
th
ep
lot.
How
man
y d
iffe
ren
t or
der
ings
of
boo
ks
can
be
chos
en?
Sin
ce e
ach
boo
k re
port
has
a d
iffe
ren
t fo
rmat
,ord
er i
s im
port
ant.
You
mu
st f
ind
the
nu
mbe
rof
per
mu
tati
ons
of 2
0 ob
ject
s ta
ken
4 a
t a
tim
e.
P(n
,r)
�P
erm
utat
ion
form
ula
P(2
0,4)
�n
�20
, r
�4
�S
impl
ify.
�D
ivid
e by
com
mon
fact
ors.
�11
6,28
0B
ooks
for
th
e bo
ok r
epor
ts c
an b
e ch
osen
116
,280
way
s.
Eva
luat
e ea
ch e
xpre
ssio
n.
1.P
(6,3
)12
02.
P(8
,5)
6720
3.P
(9,4
)30
244.
P(1
1,6)
332,
640
How
man
y d
iffe
ren
t w
ays
can
th
e le
tter
s of
eac
h w
ord
be
arra
nge
d?
5.M
OM
36.
MO
ND
AY
720
7.S
TE
RE
O36
0
8.SC
HO
OL
Th
e h
igh
sch
ool
chor
us
has
bee
n p
ract
icin
g 12
son
gs,b
ut
ther
e is
tim
e fo
r on
ly5
of t
hem
at
the
spri
ng
con
cert
.How
may
dif
fere
nt
orde
rin
gs o
f 5
son
gs a
re p
ossi
ble?
95,0
40
20 �
19 �
18 �
17 �
16 �
15 �
… �
1�
��
�16
�15
�…
�1
20!
� 16!20
!�
�(2
0 �
4)!
n!
� (n�
r)!
n!
� p!q
!
n!
� (n�
r)!
11
1
11
1
Exam
ple
Exer
cise
s
Cha
pter
12
12G
lenc
oe A
lgeb
ra 2
12-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Per
mu
tati
on
s an
d C
om
bin
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
2-2
in y
our
text
boo
k.
Su
ppos
e th
at 2
0 st
ude
nts
en
ter
a m
ath
con
test
.In
how
man
y w
ays
can
fir
st,s
econ
d,an
dth
ird
plac
es b
e aw
arde
d? (
Wri
te y
our
answ
er a
s a
prod
uct
.Do
not
cal
cula
te t
he
prod
uct
.)20
�19
�18
Rea
d t
he
Less
on
1.In
dica
te w
het
her
eac
h s
itu
atio
n i
nvo
lves
a p
erm
uta
tion
or a
com
bin
atio
n.
a.ch
oosi
ng
five
stu
den
ts f
rom
a c
lass
to
wor
k on
a s
peci
al p
roje
ctco
mb
inat
ion
b.
arra
ngi
ng
five
pic
ture
s in
a r
ow o
n a
wal
lp
erm
uta
tio
n
c.dr
awin
g a
han
d of
13
card
s fr
om a
52-
card
dec
kco
mb
inat
ion
d.
arra
ngi
ng
the
lett
ers
of t
he
wor
d al
gebr
ap
erm
uta
tio
n
2.W
rite
an
exp
ress
ion
th
at c
an b
e u
sed
to c
alcu
late
eac
h o
f th
e fo
llow
ing.
a.n
um
ber
of c
ombi
nat
ion
s of
ndi
stin
ct o
bjec
ts t
aken
rat
a t
ime� (n
�n! r)
!r!
�
b.
nu
mbe
r of
per
mu
tati
ons
of n
obje
cts
of w
hic
h p
are
alik
e an
d q
are
alik
e� pn !q! !
�
c.n
um
ber
of p
erm
uta
tion
s of
ndi
stin
ct o
bjec
ts t
aken
rat
a t
ime� (n
�n! r)
!�
3.F
ive
card
s ar
e dr
awn
fro
m a
sta
nda
rd d
eck
of c
ards
.Su
ppos
e yo
u a
re a
sked
to
dete
rmin
eh
ow m
any
poss
ible
han
ds c
onsi
st o
f on
e h
eart
,tw
o di
amon
ds,a
nd
two
spad
es.
a.W
hic
h o
f th
e fo
llow
ing
wou
ld y
ou u
se t
o so
lve
this
pro
blem
:Fu
nd
amen
tal
Cou
nti
ng
Pri
nci
ple,
perm
uta
tion
s,or
com
bin
atio
ns?
(M
ore
than
on
e of
th
ese
may
app
ly.)
Fu
nd
amen
tal C
ou
nti
ng
Pri
nci
ple
,co
mb
inat
ion
s
b.
Wri
te a
n ex
pres
sion
tha
t in
volv
es t
he n
otat
ion
P(n
,r)
and/
or C
(n,r
) th
at y
ou w
ould
use
to s
olve
th
is p
robl
em.(
Do
not
do
any
calc
ula
tion
s.)
C(1
3,1)
�C
(13,
2) �
C(1
3,2)
Rem
emb
er W
hat
Yo
u L
earn
ed
4.M
any
stu
den
ts h
ave
trou
ble
know
ing
wh
en t
o u
se p
erm
uta
tion
s an
d w
hen
to
use
com
bin
atio
ns
to s
olve
cou
nti
ng
prob
lem
s.H
ow c
an t
he
idea
of
ord
erh
elp
you
to
rem
embe
r th
e di
ffer
ence
bet
wee
n p
erm
uta
tion
s an
d co
mbi
nat
ion
s?
Sam
ple
an
swer
:A
per
mu
tati
on
is a
n a
rran
gem
ent
of
ob
ject
s in
wh
ich
ord
er is
imp
ort
ant.
A c
om
bin
atio
n is
a s
elec
tio
n o
f o
bje
cts
in w
hic
h o
rder
is n
ot
imp
ort
ant.
Chapter 12 A6 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 12-2)
Cha
pter
12
15G
lenc
oe A
lgeb
ra 2
Lesson 12-2
12-2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceP
erm
uta
tio
ns
and
Co
mb
inat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Eva
luat
e ea
ch e
xpre
ssio
n.
1.P
(6,3
)12
02.
P(8
,2)
563.
P(2
,1)
2
4.P
(3,2
)6
5.P
(10,
4)50
406.
P(5
,5)
120
7.C
(2,2
)1
8.C
(5,3
)10
9.C
(4,1
)4
10.C
(8,7
)8
11.C
(3,2
)3
12.C
(7,4
)35
Det
erm
ine
wh
eth
er e
ach
sit
uat
ion
in
volv
es a
per
mu
tati
onor
a c
ombi
na
tion
.Th
enfi
nd
th
e n
um
ber
of
pos
sib
ilit
ies.
13.s
eati
ng
8 st
ude
nts
in
8 s
eats
in
th
e fr
ont
row
of
the
sch
ool
audi
tori
um
per
mu
tati
on
;40
,320
14.i
ntr
odu
cin
g th
e 5
star
tin
g pl
ayer
s on
th
e W
oods
vill
e H
igh
Sch
ool
bask
etba
ll t
eam
at
the
begi
nn
ing
of t
he
nex
t ba
sket
ball
gam
ep
erm
uta
tio
n;
120
15.c
hec
kin
g ou
t 3
libr
ary
book
s fr
om a
lis
t of
8 b
ooks
for
a r
esea
rch
pap
erco
mb
inat
ion
;56
16.c
hoo
sin
g 2
mov
ies
to r
ent
from
5 m
ovie
sco
mb
inat
ion
;10
17.t
he
firs
t-,s
econ
d-,a
nd
thir
d-pl
ace
fin
ish
ers
in a
rac
e w
ith
10
con
test
ants
per
mu
tati
on
;72
0
18.e
lect
ing
4 ca
ndi
date
s to
a m
un
icip
al p
lan
nin
g bo
ard
from
a f
ield
of
7 ca
ndi
date
sco
mb
inat
ion
;35
19.c
hoo
sin
g 2
vege
tabl
es f
rom
a m
enu
th
at o
ffer
s 6
vege
tabl
e ch
oice
sco
mb
inat
ion
;15
20.a
n a
rran
gem
ent
of t
he
lett
ers
in t
he
wor
d rh
ombu
sp
erm
uta
tio
n;
5040
21.s
elec
tin
g 2
of 8
ch
oice
s of
ora
nge
juic
e at
a s
tore
com
bin
atio
n;
28
22.p
laci
ng
a re
d ro
se b
ush
,a y
ello
w r
ose
bush
,a w
hit
e ro
se b
ush
,an
d a
pin
k ro
se b
ush
in
aro
w i
n a
pla
nte
rp
erm
uta
tio
n;
24
23.s
elec
tin
g 2
of 9
kit
ten
s at
an
an
imal
res
cue
shel
ter
com
bin
atio
n;
36
24.a
n a
rran
gem
ent
of t
he
lett
ers
in t
he
wor
d is
osce
les
per
mu
tati
on
;30
,240
Cha
pter
12
14G
lenc
oe A
lgeb
ra 2
12-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Per
mu
tati
on
s an
d C
om
bin
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
Co
mb
inat
ion
sA
n a
rran
gem
ent
or s
elec
tion
of
obje
cts
in w
hic
h o
rder
is
not
impo
rtan
t is
call
ed a
com
bin
atio
n.
Co
mb
inat
ion
sT
he n
umbe
r of
com
bina
tions
of n
dist
inct
obj
ects
take
n r
at a
tim
e is
giv
en b
y C
(n, r
) �
.
SCH
OO
LH
ow m
any
grou
ps
of 4
stu
den
ts c
an b
e se
lect
ed f
rom
acl
ass
of 2
0?S
ince
th
e or
der
of c
hoo
sin
g th
e st
ude
nts
is
not
im
port
ant,
you
mu
st f
ind
the
nu
mbe
r of
com
bin
atio
ns
of 2
0 st
ude
nts
tak
en 4
at
a ti
me.
C(n
,r)
�C
ombi
natio
n fo
rmul
a
C(2
0,4)
�n
�20
, r
�4
�or
484
5
Th
ere
are
4845
pos
sibl
e w
ays
to c
hoo
se 4
stu
den
ts.
In h
ow m
any
way
s ca
n y
ou c
hoo
se 1
vow
el a
nd
2 c
onso
nan
ts f
rom
ase
t of
26
lett
er t
iles
? (A
ssu
me
ther
e ar
e 5
vow
els
and
21
con
son
ants
.)B
y th
e F
un
dam
enta
l C
oun
tin
g P
rin
cipl
e,yo
u c
an m
ult
iply
th
e n
um
ber
of w
ays
to s
elec
t on
evo
wel
an
d th
e n
um
ber
of w
ays
to s
elec
t 2
con
son
ants
.On
ly t
he
lett
ers
chos
en m
atte
r,n
otth
e or
der
in w
hic
h t
hey
wer
e ch
osen
,so
use
com
bin
atio
ns.
C(5
,1)
On
e of
5 v
owel
s ar
e dr
awn
.C
(21,
2)T
wo
of 2
1 co
nso
nan
ts a
re d
raw
n.
C(5
,1)
�C
(21,
2) �
�C
ombi
natio
n fo
rmul
a
��
Sub
trac
t.
�5
�21
0 or
105
0S
impl
ify.
Th
ere
are
1050
com
bin
atio
ns
of 1
vow
el a
nd
2 co
nso
nan
ts.
Eva
luat
e ea
ch e
xpre
ssio
n.
1.C
(5,3
)10
2.C
(7,4
)35
3.C
(15,
7)64
354.
C(1
0,5)
252
5.PL
AY
ING
CA
RD
SF
rom
a s
tan
dard
dec
k of
52
card
s,in
how
man
y w
ays
can
5 c
ards
be
draw
n?
2,59
8,96
0
6.H
OC
KEY
How
man
y h
ocke
y te
ams
of 6
pla
yers
can
be
form
ed f
rom
14
play
ers
wit
hou
tre
gard
to
posi
tion
pla
yed?
3003
7.C
OM
MIT
TEES
Fro
m a
gro
up
of 1
0 m
en a
nd
12 w
omen
,how
man
y co
mm
itte
es o
f 5
men
and
6 w
omen
can
be
form
ed?
232,
848
21!
� 19!2
!5! � 4!
21!
��
(21
�2)
!2!
5!�
�(5
�1)
!1!
20!
� 16!4
!20!
��
(20
�4)
!4!
n!
��
(n�
r)!r
!
n!
��
(n�
r)!r
!
Exam
ple
1
Exam
ple
2
Exer
cise
s
Chapter 12 A7 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 12-2)
Cha
pter
12
17G
lenc
oe A
lgeb
ra 2
Lesson 12-2
12-2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Per
mu
tati
on
s an
d C
om
bin
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1.W
AIT
ING
IN
LIN
EW
hen
th
e 12
stu
den
ts i
n M
r.Ja
ybir
d’s
clas
s go
to
lun
ch,t
hey
for
m a
sin
gle
file
lin
e.D
oes
form
ing
a li
ne
invo
lve
a pe
rmu
tati
on
or a
com
bin
atio
n o
f th
e st
ude
nts
?A
per
mu
tati
on
2.A
RT
Isab
el n
eeds
to
sele
ct t
hre
edi
ffer
ent
colo
rs o
f co
nst
ruct
ion
pap
er t
om
ake
a fl
ag f
or a
sch
ool
proj
ect.
Sh
e ca
nch
oose
fro
m a
sel
ecti
on o
f 15
dif
fere
nt
colo
rs.I
n h
ow m
any
way
s ca
n s
he
pick
her
col
ors?
455
3.SU
DO
KU
A p
opu
lar
gam
e ca
lled
“Su
doku
”in
volv
es s
quar
e ar
rays
of
nu
mbe
rs.I
n a
gam
e of
Su
doku
,eve
ryen
try
is a
n i
nte
ger
betw
een
1 a
nd
9,in
clu
sive
.No
nu
mbe
r ap
pear
s tw
ice
in a
ny
row
or
colu
mn
.
For
a g
ame
of S
udo
ku,h
ow m
any
diff
eren
t po
ssib
ilit
ies
are
ther
e fo
r th
efi
rst
row
of
nu
mbe
rs?
362,
880
71
86
94
23
5
92
57
31
64
8
46
38
52
79
1
59
21
73
48
6
83
14
65
92
7
97
42
89
51
3
34
95
17
86
2
28
73
46
15
9
15
69
28
37
4
4.N
AM
ESH
ann
ah i
s cu
riou
s to
kn
owh
ow m
any
diff
eren
t 6
lett
er s
equ
ence
ssh
e ca
n m
ake
usi
ng
each
of
the
lett
ers
of h
er n
ame
exac
tly
once
.For
exa
mpl
e,“H
AN
NA
H,”
“AA
HH
NN
,”an
d“N
AH
NA
H”
are
all
poss
ible
seq
uen
ces.
How
man
y to
tal
sequ
ence
s ar
e po
ssib
le?
90
MET
EOR
ITES
For
Exe
rcis
es 5
an
d 6
,use
the
foll
owin
g in
form
atio
n.
Ove
r th
e co
urs
e of
sev
eral
yea
rs,K
endr
am
anag
ed t
o co
llec
t 7
met
eori
tes.
Eac
h o
ne
is u
niq
ue.
5.F
or a
sch
ool
scie
nce
fai
r,K
endr
adi
spla
ys h
er m
eteo
rite
s in
a r
ow.H
owm
any
way
s ar
e th
ere
to o
rder
th
em
eteo
rite
s?50
40
6.S
he
deci
des
to t
rade
th
ree
of h
erm
eteo
rite
s fo
r a
tele
scop
e af
ter
the
fair
.How
man
y w
ays
can
sh
e pi
ck o
ut
3 m
eteo
rite
s fr
om h
er c
olle
ctio
n?
35
Cha
pter
12
16G
lenc
oe A
lgeb
ra 2
12-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Prac
tice
Per
mu
tati
on
s an
d C
om
bin
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Eva
luat
e ea
ch e
xpre
ssio
n.
1.P
(8,6
)20
,160
2.P
(9,7
)18
1,44
03.
P(3
,3)
6
4.P
(4,3
)24
5.P
(4,1
)4
6.P
(7,2
)42
7.C
(8,2
)28
8.C
(11,
3)16
59.
C(2
0,18
)19
0
10.C
(9,9
)1
11.C
(3,1
)3
12.C
(9,3
) �
C(6
,2)
1260
Det
erm
ine
wh
eth
er e
ach
sit
uat
ion
in
volv
es a
per
mu
tati
onor
a c
ombi
na
tion
.Th
enfi
nd
th
e n
um
ber
of
pos
sib
ilit
ies.
13.s
elec
tin
g a
4-pe
rson
bob
sled
tea
m f
rom
a g
rou
p of
9 a
thle
tes
com
bin
atio
n;
126
14.a
n a
rran
gem
ent
of t
he
lett
ers
in t
he
wor
d C
anad
ap
erm
uta
tio
n;
120
15.a
rran
gin
g 4
char
ms
on a
bra
cele
t th
at h
as a
cla
sp,a
fro
nt,
and
a ba
ckp
erm
uta
tio
n;
24
16.s
elec
tin
g 3
dess
erts
fro
m 1
0 de
sser
ts t
hat
are
dis
play
ed o
n a
des
sert
car
t in
a r
esta
ura
nt
com
bin
atio
n;
120
17.a
n a
rran
gem
ent
of t
he
lett
ers
in t
he
wor
d an
nu
ally
per
mu
tati
on
;50
40
18.f
orm
ing
a 2-
pers
on s
ales
tea
m f
rom
a g
rou
p of
12
sale
speo
ple
com
bin
atio
n;
66
19.m
akin
g 5-
side
d po
lygo
ns b
y ch
oosi
ng a
ny 5
of
11 p
oint
s lo
cate
d on
a c
ircl
e to
be
the
vert
ices
com
bin
atio
n;
462
20.s
eati
ng
5 m
en a
nd
5 w
omen
alt
ern
atel
y in
a r
ow,b
egin
nin
g w
ith
a w
oman
per
mu
tati
on
;14
,400
21.S
TUD
ENT
GR
OU
PSFa
rmin
gton
Hig
h i
s pl
ann
ing
its
acad
emic
fes
tiva
l.A
ll m
ath
clas
ses
wil
l se
nd
2 re
pres
enta
tive
s to
com
pete
in
th
e m
ath
bow
l.H
ow m
any
diff
eren
tgr
oups
of
stu
den
ts c
an b
e ch
osen
fro
m a
cla
ss o
f 16
stu
den
ts?
120
22.P
HO
TOG
RA
PHY
A p
hot
ogra
pher
is
taki
ng
pict
ure
s of
a b
ride
an
d gr
oom
an
d th
eir
6at
ten
dan
ts.I
f sh
e ta
kes
phot
ogra
phs
of 3
peo
ple
in a
gro
up,
how
man
y di
ffer
ent
grou
psca
n s
he
phot
ogra
ph?
56
23.A
IRLI
NES
An
air
lin
e is
hir
ing
5 fl
igh
t at
ten
dan
ts.I
f 8
peop
le a
pply
for
th
e jo
b,h
owm
any
diff
eren
t gr
oups
of
5 at
ten
dan
ts c
an t
he
airl
ine
hir
e?56
24.S
UB
SCR
IPTI
ON
SA
sch
ool
libr
aria
n w
ould
lik
e to
bu
y su
bscr
ipti
ons
to 7
new
mag
azin
es.H
er b
udg
et,h
owev
er,w
ill
allo
w h
er t
o bu
y on
ly 4
new
su
bscr
ipti
ons.
How
man
y di
ffer
ent
grou
ps o
f 4
mag
azin
es c
an s
he
choo
se f
rom
th
e 7
mag
azin
es?
35
Chapter 12 A8 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 12-2)
Cha
pter
12
19G
lenc
oe A
lgeb
ra 2
Lesson 12-2
12-2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Spre
adsh
eet
Act
ivit
yP
erm
uta
tio
ns
and
Co
mb
inat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
You
hav
e le
arn
ed t
he
form
ula
s fo
r th
e n
um
ber
of p
erm
uta
tion
s of
nob
ject
sta
ken
rat
a t
ime,
P(n
,r),
and
the
nu
mbe
r of
com
bin
atio
ns
of n
obje
cts
take
nr
at a
tim
e,C
(n,r
).Yo
u a
re g
oin
g to
set
up
a sp
read
shee
t li
ke t
he
one
show
nbe
low
to
perf
orm
an
alys
es o
f th
ese
fun
ctio
ns.
In t
he
spre
adsh
eet,
the
valu
es i
n r
ow 1
rep
rese
nt
n,t
he
valu
es i
n r
ow 2
re
pres
ent
r,an
d th
e fo
rmu
las
for
P(n
,r)
and
C(n
,r)
are
in r
ows
3 an
d 4,
resp
ecti
vely
.
Th
e fo
rmu
la t
o ca
lcu
late
P(n
,r)
is�
FA
CT
(B1)
/FA
CT
(B1-
B2)
.
FA
CT
is a
spe
cial
fu
nct
ion
fro
m t
he
fun
ctio
n l
ist
and
shou
ld n
ot b
e en
tere
dfr
om t
he
lett
ers
on t
he
keyb
oard
.En
ter
the
form
ula
in
B3.
Th
en d
rag
the
curs
or a
cros
s th
e ro
w t
o co
py t
he
form
ula
in
to c
ells
C3
thro
ugh
G3.
Th
e fo
rmu
la f
or C
(n,r
) is
�F
AC
T(B
1)/(
FA
CT
(B1�
B2)
*FA
CT
(B2)
) an
d sh
ould
be e
nte
red
in c
ell
B4.
Cop
y th
e fo
rmu
la i
nto
cel
ls C
4 th
rou
gh G
4.
1.C
ompa
re t
he
valu
es o
f P
(n,r
) an
d C
(n,r
) fo
r n
�5
and
r�
0 th
rou
gh 5
,as
wel
l as
for
tw
o ot
her
ch
oice
s of
nan
d r.
Mo
st o
f th
e va
lues
of
P(n
,r)
are
mu
ch la
rger
th
an t
he
corr
esp
on
din
g v
alu
es o
f C
(n,r
).T
he
valu
es o
f P
(n,r
) te
nd
to
incr
ease
,wh
ile t
he
valu
es o
f C
(n,r
)te
nd
to
incr
ease
an
d t
hen
dec
reas
e.
2.S
ever
al i
den
titi
es h
old
for
P(n
,r)
and
C(n
,r).
Use
th
e sp
read
shee
t to
ver
ify
the
foll
owin
g id
enti
ties
by
fin
din
g th
ree
exam
ples
of
each
.2a
-2c.
See
stu
den
ts’w
ork
.a.
P(n
,n)�
P(n
,n�
1)
b.C
(n�
1,r)
�C
(n,r
�1)
�C
(n,r
)
c.C
(n,0
)�C
(n,1
)�C
(n,2
)�..
.�C
(n,n
)�2n
A1 32 4 5
BC
DE
FG
n r P (
n , r
)C
(n
, r)
5 0 1 1
5 1 5 5
5 2 20 10
5 3 60 10
5 412
0 5
5 512
0 1
Sh
eet
1S
hee
t 2
Sh
eet
3
Exer
cise
s
Cha
pter
12
18G
lenc
oe A
lgeb
ra 2
12-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
Co
mb
inat
ion
s an
d P
asca
l’s T
rian
gle
Pas
cal’s
tri
angl
e is
a s
peci
al a
rray
of
nu
mbe
rs i
nve
nte
d by
Bla
ise
Pas
cal
(162
3–16
62).
Th
e va
lues
in
Pas
cal’s
tri
angl
e ca
n b
e fo
un
d u
sin
g th
eco
mbi
nat
ion
s sh
own
bel
ow.
1.E
valu
ate
the
expr
essi
on i
n e
ach
cel
l of
th
e tr
ian
gle.
2.T
he p
atte
rn s
how
s th
e re
lati
onsh
ip b
etw
een
C(n
,r)
and
Pas
cal’s
tri
angl
e.In
gen
eral
,it
is t
rue
that
C(n
,r)
�C
(n,r
�1)
�C
(n�
1,r
�1)
.Com
plet
eth
e pr
oof
of t
his
pro
pert
y.In
eac
h s
tep,
the
den
omin
ator
has
bee
n g
iven
.
C(n
,r)
�C
(n,r
�1)
��
��
��
� � � � �C
(n�
1,r
�1)
(n�
1)!
(r�
1)![
(n�
1) �
(r�
1)]!
(n�
1)!
(r�
1)!(
n�
r)!
n!(
n�
1)(r
�1)
!(n
�r)
!
n!(
r�
1 �
n�
r)(r
�1)
!(n
�r)
!
n!(
n�
r)(r
�1)
!(n
�r)
!n
!(r
�1)
(r�
1)!(
n�
r)!
n!(
n�
r)(r
�1)
!(n
�r
�1)
!(n
�r)
n!(
r�
1)r!
(n�
r)!(
r�
1)
n!
(r�
1)!(
n�
r�
1)!
n!
r!(n
�r)
!
C(1
,0)
1
C(1
,1)
1C
(2,0
)
1
C(2
,1)
2
C(2
,2)
1
C(3
,0)
1
C(3
,1)
3
C(3
,2)
3
C(3
,3)
1C
(4,0
)
1
C(4
,1)
4
C(4
,2)
6
C(4
,3)
4
C(4
,4)
1
C(5
,0)
1
C(5
,1)
5
C(5
,2)
10
C(5
,3)
10
C(5
,4)
5
C(5
,5)
1
Chapter 12 A9 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 12-3)
Cha
pter
12
21G
lenc
oe A
lgeb
ra 2
Lesson 12-3
12-3
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Pro
bab
ility
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
Pro
bab
ility
an
d O
dd
sIn
pro
babi
lity
,a d
esir
ed o
utc
ome
is c
alle
d a
succ
ess;
any
oth
erou
tcom
e is
cal
led
a fa
ilu
re.
Pro
bab
ility
of
If an
eve
nt c
an s
ucce
ed in
sw
ays
and
fail
in f
way
s, t
hen
the
prob
abili
ties
of s
ucce
ss,
P(S
),
Su
cces
s an
dan
d of
fai
lure
, P
(F),
are
as
follo
ws.
Failu
reP
(S)
�an
d P
(F)
�.
Def
init
ion
If an
eve
nt c
an s
ucce
ed in
sw
ays
and
fail
in f
way
s, t
hen
the
odds
of
succ
ess
and
of f
ailu
re a
re
of
Od
ds
as f
ollo
ws.
Odd
s of
suc
cess
�s
:fO
dds
of f
ailu
re �
f:s
Wh
en 3
coi
ns
are
toss
ed,w
hat
is
the
pro
bab
ilit
y th
at a
t le
ast
2 ar
e h
ead
s?Yo
u c
an u
se a
tre
e di
agra
m t
o fi
nd
the
sam
ple
spac
e.O
f th
e 8
poss
ible
ou
tcom
es,4
hav
e at
lea
st 2
hea
ds.S
o th
e
prob
abil
ity
of t
ossi
ng
at l
east
2 h
eads
is
�4 8�or
�1 2� .
Wh
at i
s th
e p
rob
abil
ity
of p
ick
ing
4 fi
ctio
n b
ook
s an
d 2
bio
grap
hie
sfr
om a
bes
t-se
ller
lis
t th
at c
onsi
sts
of 1
2 fi
ctio
n b
ook
s an
d 6
bio
grap
hie
s?B
y th
e F
un
dam
enta
l C
oun
tin
g P
rin
cipl
e,th
e n
um
ber
of s
ucc
esse
s is
C(1
2,4)
�C
(6,2
).T
he
tota
l n
um
ber
of s
elec
tion
s,s
�f,
of 6
boo
ks i
s C
(18,
6).
P(4
fic
tion
,2 b
iogr
aph
y) �
or a
bou
t 0.
40
Th
e pr
obab
ilit
y of
sel
ecti
ng
4 fi
ctio
n b
ooks
an
d 2
biog
raph
ies
is a
bou
t 40
%.
Fin
d t
he
odd
s of
an
eve
nt
occu
rrin
g,gi
ven
th
e p
rob
abil
ity
of t
he
even
t.
1.�3 7�
3:4
2.�4 5�
4:1
3.� 12 3�
2:11
4.1:
14
Fin
d t
he
pro
bab
ilit
y of
an
eve
nt
occu
rrin
g,gi
ven
th
e od
ds
of t
he
even
t.
5.10
:1�1 10 1�
6.2:
5�2 7�
7.4:
9� 14 3�
8.8:
3� 18 1�
On
e b
ag o
f ca
nd
y co
nta
ins
15 r
ed c
and
ies,
10 y
ello
w c
and
ies,
and
6 g
reen
can
die
s.F
ind
th
e p
rob
abil
ity
of e
ach
sel
ecti
on.
9.pi
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red
can
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10.n
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icki
ng
a ye
llow
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icki
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een
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12.n
ot p
icki
ng
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d ca
ndy
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2,4)
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6)
HH
HH
HT
HT
HH
TT
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HT
HT
TT
HT
TT
H T H T H T H T
H T
H T H T
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inP
oss
ible
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s� s
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Exam
ple
1
Exam
ple
2
Exer
cise
s
Cha
pter
12
20G
lenc
oe A
lgeb
ra 2
12-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Pro
bab
ility
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
2-3
in y
our
text
boo
k.
Wh
at i
s th
e pr
obab
ilit
y th
at a
per
son
wil
l n
otbe
str
uck
by
ligh
tnin
g in
a g
iven
yea
r?
�7 74 59 0, ,9 09 09 0�
Rea
d t
he
Less
on
1.In
dica
te w
het
her
eac
h o
f th
e fo
llow
ing
stat
emen
ts i
s tr
ue
or f
alse
.
a.If
an
eve
nt
can
nev
er o
ccu
r,it
s pr
obab
ilit
y is
a n
egat
ive
nu
mbe
r.fa
lse
b.
If a
n e
ven
t is
cer
tain
to
hap
pen
,its
pro
babi
lity
is
1.tr
ue
c.If
an
eve
nt
can
su
ccee
d in
sw
ays
and
fail
in
fw
ays,
then
th
e pr
obab
ilit
y of
su
cces
s
is
.fa
lse
d.
If a
n e
ven
t ca
n s
ucc
eed
in s
way
s an
d fa
il i
n f
way
s,th
en t
he
odds
aga
inst
th
e ev
ent
are
s:f.
fals
e
e.A
pro
babi
lity
dis
trib
uti
on i
s a
fun
ctio
n i
n w
hic
h t
he
dom
ain
is
the
sam
ple
spac
e of
an
expe
rim
ent.
tru
e
2.A
wea
ther
for
ecas
t sa
ys t
hat
th
e ch
ance
of
rain
tom
orro
w i
s 40
%.
a.W
rite
th
e pr
obab
ilit
y th
at i
t w
ill
rain
tom
orro
w a
s a
frac
tion
in
low
est
term
s.�2 5�
b.
Wri
te t
he
prob
abil
ity
that
it
wil
l n
ot r
ain
tom
orro
w a
s a
frac
tion
in
low
est
term
s.�3 5�
c.W
hat
are
th
e od
ds i
n f
avor
of
rain
?2:
3
d.
Wh
at a
re t
he
odds
aga
inst
rai
n?
3:2
3.R
efer
to
the
tabl
e in
Exa
mpl
e 4
on p
age
646
in y
our
text
book
.
a.W
hat
oth
er s
um
has
th
e sa
me
prob
abil
ity
as a
su
m o
f 11
?3
b.
Wh
at a
re t
he
odds
of
roll
ing
a su
m o
f 8?
5:31
c.W
hat
are
th
e od
ds a
gain
st r
olli
ng
a su
m o
f 9?
8:1
Rem
emb
er W
hat
Yo
u L
earn
ed
4.A
goo
d w
ay t
o re
mem
ber
som
eth
ing
is t
o ex
plai
n i
t to
som
eon
e el
se.S
upp
ose
that
you
rfr
ien
d R
ober
to i
s h
avin
g tr
oubl
e re
mem
beri
ng
the
diff
eren
ce b
etw
een
pro
babi
lity
an
dod
ds.W
hat
wou
ld y
ou t
ell
him
to
hel
p h
im r
emem
ber
this
eas
ily?
Sam
ple
an
swer
:P
rob
abili
ty g
ives
th
e ra
tio
of
succ
esse
s to
th
e to
tal
nu
mb
er o
f o
utc
om
es,w
hile
od
ds
giv
es t
he
rati
o o
f su
cces
ses
to f
ailu
res.
s � f
Chapter 12 A10 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 12-3)
Cha
pter
12
23G
lenc
oe A
lgeb
ra 2
Lesson 12-3
12-3
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceP
rob
abili
ty
NA
ME
____
____
____
____
____
____
____
____
____
____
____
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ATE
____
____
____
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IOD
____
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Ah
med
is
pos
tin
g 2
ph
otog
rap
hs
on h
is w
ebsi
te.H
e h
as n
arro
wed
his
ch
oice
s to
4la
nd
scap
e p
hot
ogra
ph
s an
d 3
por
trai
ts.I
f h
e ch
oose
s th
e tw
o p
hot
ogra
ph
s at
ran
dom
,fin
d t
he
pro
bab
ilit
y of
eac
h s
elec
tion
.
1.P
(2 p
ortr
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of
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e C
aru
bas
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ecti
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vid
eo m
ovie
s,in
clu
din
g 12
wes
tern
s an
d
16 s
cien
ce f
icti
on.E
lise
sel
ects
3 o
f th
e m
ovie
s at
ran
dom
to
bri
ng
to a
sle
ep-o
ver
at h
er f
rien
d’s
hou
se.F
ind
th
e p
rob
abil
ity
of e
ach
sel
ecti
on.
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(3 w
este
rns)
� 85 15 9�5.
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ence
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tion
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ce f
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nce
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tion
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8.P
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(2 s
cien
ce f
icti
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nd
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este
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For
Exe
rcis
es 1
0–13
,use
th
e ch
art
that
sh
ows
the
clas
s an
d g
end
er s
tati
stic
s fo
r th
e st
ud
ents
tak
ing
an
Alg
ebra
1 o
r A
lgeb
ra 2
cla
ss a
t L
a M
esa
Hig
h S
choo
l.If
a s
tude
nt
taki
ng
Alg
ebra
1 o
r A
lgeb
ra 2
is
sele
cted
at
ran
dom
,fin
d ea
ch p
roba
bili
ty.E
xpre
ss a
s de
cim
als
rou
nde
d to
th
e n
eare
st t
hou
san
dth
.
10.P
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hom
ore/
fem
ale)
0.20
8
11.P
(ju
nio
r/m
ale)
0.14
3
12.P
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shm
an/m
ale)
0.13
6
13.P
(fre
shm
an/f
emal
e)0.
145
Fin
d t
he
odd
s of
an
eve
nt
occu
rrin
g,gi
ven
th
e p
rob
abil
ity
of t
he
even
t.
14.�
5 8�5:
315
.�2 7�
2:5
16.�
3 5�3:
2
17.�
11 0�1:
918
.�5 6�
5:1
19.�
15 2�5:
7
Fin
d t
he
pro
bab
ilit
y of
an
eve
nt
occu
rrin
g,gi
ven
th
e od
ds
of t
he
even
t.
20.2
:1�2 3�
21.8
:9� 18 7�
22.4
:1�4 5�
23.1
:9� 11 0�
24.2
:7�2 9�
25.5
:9� 15 4�
Cla
ss/G
end
erN
um
ber
Fres
hman
/Mal
e95
Fres
hman
/Fem
ale
101
Sop
hom
ore/
Mal
e15
4
Sop
hom
ore/
Fem
ale
145
Juni
or/M
ale
100
Juni
or/F
emal
e10
2
Cha
pter
12
22G
lenc
oe A
lgeb
ra 2
12-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Pro
bab
ility
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Pro
bab
ility
Dis
trib
uti
on
sA
ran
dom
var
iab
leis
a v
aria
ble
wh
ose
valu
e is
th
en
um
eric
al o
utc
ome
of a
ran
dom
eve
nt.
A p
rob
abil
ity
dis
trib
uti
onfo
r a
part
icu
lar
ran
dom
vari
able
is
a fu
nct
ion
th
at m
aps
the
sam
ple
spac
e to
th
e pr
obab
ilit
ies
of t
he
outc
omes
in
th
esa
mpl
e sp
ace.
Su
pp
ose
two
dic
e ar
e ro
lled
.Th
e ta
ble
an
d t
he
rela
tive
-fre
qu
ency
his
togr
am s
how
th
e d
istr
ibu
tion
of
the
abso
lute
val
ue
of t
he
dif
fere
nce
of
the
nu
mb
ers
roll
ed.U
se t
he
grap
h t
o d
eter
min
e w
hic
h o
utc
ome
is t
he
mos
t li
kel
y.W
hat
is
its
pro
bab
ilit
y?
Th
e gr
eate
st p
roba
bili
ty i
n t
he
grap
h i
s � 15 8�
.
Th
e m
ost
like
ly o
utc
ome
is a
dif
fere
nce
of
1 an
d it
s
prob
abil
ity
is � 15 8�
.
Fou
r co
ins
are
toss
ed.
1.C
ompl
ete
the
tabl
e be
low
to
show
th
e pr
obab
ilit
y di
stri
buti
on o
f th
e n
um
ber
of h
eads
.
2.M
ake
rela
tive
-fre
quen
cy d
istr
ibu
tion
of
the
data
.
10
Hea
ds
Head
s in
Co
in T
oss
23
4
1 4
Probability
3 8 1 8 1 163 165 16Nu
mb
er o
f H
ead
s0
12
34
Pro
bab
ility
� 11 6��1 4�
�3 8��1 4�
� 11 6�
00
Probability
Dif
fere
nce
Nu
mb
ers
Sh
ow
ing
on
th
e D
ice
12
34
5
1 6 1 92 9 1 185 18
Dif
fere
nce
01
23
45
Pro
bab
ility
�1 6�� 15 8�
�2 9��1 6�
�1 9�� 11 8�
Exam
ple
Exer
cise
s
Chapter 12 A11 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 12-3)
Cha
pter
12
25G
lenc
oe A
lgeb
ra 2
Lesson 12-3
12-3
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Pro
bab
ility
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1.A
RT
Th
e le
tter
s “A
”,“R
”,an
d “T
”ar
ew
ritt
en o
n t
hre
e di
ffer
ent
piec
es o
fpa
per.
Th
e pi
eces
of
pape
r ar
e th
en p
ut
in a
bag
an
d m
ixed
up.
Log
an p
icks
eac
hle
tter
wit
hou
t lo
okin
g an
d pl
aces
th
emsi
de b
y si
de.W
hat
is
the
prob
abil
ity
that
the
lett
ers
spel
l “A
RT
”?
2.A
GE
Th
ere
are
24 s
tude
nts
in
Mis
sM
ason
’s t
hir
d gr
ade
clas
s,al
l bo
rn o
ndi
ffer
ent
days
.Ele
ven
stu
den
ts a
re b
oys.
In t
he
mor
nin
g,th
e cl
assr
oom
is
empt
y.O
ne
stu
den
t ar
rive
s fo
llow
ed b
y an
oth
er.
Wh
at i
s th
e pr
obab
ilit
y th
at w
hen
th
efi
rst
two
stu
den
ts a
rriv
e,on
e is
a b
oyan
d th
e ot
her
a g
irl?
52%
3.D
ICE
Jam
al r
olls
tw
o si
x-si
ded
dice
,on
eaf
ter
the
oth
er.W
hat
is
the
prob
abil
ity
that
th
e se
con
d di
e sh
ows
a n
um
ber
larg
er t
han
th
e fi
rst
die?
4.LA
NG
UA
GES
Noa
h c
ann
ot d
ecid
ew
het
her
to
lear
n F
ren
ch,G
erm
an,
Ital
ian
,Ru
ssia
n,o
r C
hin
ese.
He
assi
gns
each
lan
guag
e a
diff
eren
t n
um
ber
from
0
to 4
.He
then
tak
es f
our
fair
coi
ns
and
flip
s th
em.H
e de
cide
d to
tak
e th
ela
ngu
age
corr
espo
ndi
ng
to t
he
nu
mbe
rof
coi
ns
that
com
e u
p h
eads
.Doe
s N
oah
’sm
eth
od f
or c
hoo
sin
g a
lan
guag
e gi
veea
ch l
angu
age
the
sam
e ch
ance
of
bein
gch
osen
? E
xpla
in.
No
.Fo
r ex
amp
le,t
he
pro
bab
ility
of
get
tin
g 0
is 1
in 1
6 bu
t th
ep
rob
abili
ty o
f g
etti
ng
1 is
1 in
4.
5 � 121 � 6
ICE
CR
EAM
For
Exe
rcis
es 5
-7,u
se t
he
foll
owin
g in
form
atio
n.
A s
urv
ey o
f th
e st
ude
nts
in
Mr.
Orr
’s f
ifth
grad
e cl
ass
aske
d ea
ch s
tude
nt
to n
ame
thei
r fa
vori
te f
lavo
r of
ice
cre
am.T
he
resu
lts
are
show
n i
n t
he
tabl
e be
low
.
5.A
stu
den
t fr
om M
r.O
rr’s
cla
ss i
sse
lect
ed a
t ra
ndo
m.W
hat
is
the
prob
abil
ity
that
th
e st
ude
nt’s
fav
orit
efl
avor
of
ice
crea
m i
s ch
ocol
ate?
6.A
stu
den
t fr
om M
r.O
rr’s
cla
ss i
sse
lect
ed a
t ra
ndo
m.W
hat
is
the
prob
abil
ity
that
th
e st
ude
nt’s
fav
orit
efl
avor
of
ice
crea
m i
s ba
nan
a?
7.A
stu
den
t fr
om M
r.O
rr’s
cla
ss i
sse
lect
ed a
t ra
ndo
m.I
s it
mor
e li
kely
th
atth
e st
ude
nt
pref
ers
eith
er b
utt
ern
ut
orst
raw
berr
y or
th
at t
he
stu
den
t pr
efer
sei
ther
ch
ocol
ate
or b
anan
a?C
ho
cola
te o
r b
anan
a is
mo
relik
ely.
1 � 303 � 10
Fla
vor
Nu
mb
er o
f S
tud
ents
Van
illa
10
Cho
cola
te9
But
tern
ut5
Str
awbe
rry
4
Ban
ana
1
Cof
fee
1
Cha
pter
12
24G
lenc
oe A
lgeb
ra 2
12-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Prac
tice
Pro
bab
ility
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
A b
ag c
onta
ins
1 gr
een
,4 r
ed,a
nd
5 y
ello
w b
alls
.Tw
o b
alls
are
sel
ecte
d a
tra
nd
om.F
ind
th
e p
rob
abil
ity
of e
ach
sel
ecti
on.
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(2 r
ed)
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P(1
red
an
d 1
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ow)
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en a
nd
1 ye
llow
)�1 9�
4.P
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reen
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5.P
(2 r
ed a
nd
1 ye
llow
)0
6.P
(1 r
ed a
nd
1 gr
een
)� 44 5�
A b
ank
con
tain
s 3
pen
nie
s,8
nic
kel
s,4
dim
es,a
nd
10
qu
arte
rs.T
wo
coin
s ar
ese
lect
ed a
t ra
nd
om.F
ind
th
e p
rob
abil
ity
of e
ach
sel
ecti
on.
7.P
(2 p
enn
ies)
� 11 00�8.
P(2
dim
es)
� 51 0�9.
P(1
nic
kel
and
1 di
me)
� 78 5�
10.P
(1 q
uar
ter
and
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nn
y)11
.P(1
qu
arte
r an
d 1
nic
kel)
12.P
(2 d
imes
an
d 1
quar
ter)
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0
Hen
rico
vis
its
a h
ome
dec
orat
ing
stor
e to
ch
oose
wal
lpap
ers
for
his
new
hou
se.T
he
stor
e h
as 2
8 b
ook
s of
wal
lpap
er s
amp
les,
incl
ud
ing
10 b
ook
s of
Wal
lPri
de
sam
ple
san
d 1
8 b
ook
s of
Del
uxe
Wal
l C
over
ings
sam
ple
s.T
he
stor
e w
ill
allo
w H
enri
co t
ob
rin
g 4
boo
ks
hom
e fo
r a
few
day
s so
he
can
dec
ide
wh
ich
wal
lpap
ers
he
wan
ts t
ob
uy.
If H
enri
co r
and
omly
ch
oose
s 4
boo
ks
to b
rin
g h
ome,
fin
d t
he
pro
bab
ilit
y of
each
sel
ecti
on.
13.P
(4 W
allP
ride
)� 12 95�
14.P
(2 W
allP
ride
an
d 2
Del
uxe
)�1 45 53 5�
15.P
(1 W
allP
ride
an
d 3
Del
uxe
)� 15 34 64 5
�16
.P(3
Wal
lPri
de a
nd
1 D
elu
xe)
� 44 58 5�
For
Exe
rcis
es 1
7–20
,use
th
e ta
ble
th
at s
how
s th
e ra
nge
of
ver
bal
SA
T s
core
s fo
rfr
esh
men
at
a sm
all
lib
eral
arts
col
lege
.If
a fr
esh
man
stu
den
t is
ch
osen
at
ran
dom
,fin
d e
ach
pro
bab
ilit
y.E
xpre
ss a
s d
ecim
als
rou
nd
ed t
o th
e n
eare
st t
hou
san
dth
.
17.P
(400
–449
)0.
052
18.P
(550
–559
)0.
243
19.P
(at
leas
t 65
0)0.
166
Fin
d t
he
odd
s of
an
eve
nt
occu
rrin
g,gi
ven
th
e p
rob
abil
ity
of t
he
even
t.
20.�
14 1�4:
721
.�1 12 3�
12:1
22.�
95 9�5:
9423
.�10
1 00�1:
999
24.�
15 6�5:
1125
.�93 5�
3:92
26.�
79 0�9:
6127
.�18 5�
8:7
Fin
d t
he
pro
bab
ilit
y of
an
eve
nt
occu
rrin
g,gi
ven
th
e od
ds
of t
he
even
t.
28.2
:23
� 22 5�29
.2:5
�2 7�30
.15:
1�1 15 6�
31.9
:7� 19 6�
32.1
1:14
�1 21 5�33
.100
0:1
�1 10 00 00 1�
34.1
2:17
�1 22 9�35
.8:1
3� 28 1�
Ran
ge
400–
449
450–
499
500–
549
550–
559
600–
649
650�
Nu
mb
er o
f S
tud
ents
129
275
438
602
620
412
Chapter 12 A12 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lessons 12-3 and 12-4)
Cha
pter
12
27G
lenc
oe A
lgeb
ra 2
Lesson 12-4
12-4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Mu
ltip
lyin
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
2-4
in y
our
text
boo
k.
Wri
te t
he
prob
abil
ity
that
Yao
Min
g m
ade
a fi
eld
goal
sh
ot d
uri
ng
the
2004
�05
sea
son
as
afr
acti
on i
n l
owes
t te
rms.
(You
r an
swer
sh
ould
not
in
clu
de a
dec
imal
.)
Rea
d t
he
Less
on
1.A
bag
con
tain
s 4
yell
ow b
alls
,5 r
ed b
alls
,1 w
hit
e ba
ll,a
nd
2 bl
ack
ball
s.A
ball
is
draw
nfr
om t
he
bag
and
is n
ot r
epla
ced.
Ase
con
d ba
ll i
s dr
awn
.
a.L
et Y
be t
he
even
t “f
irst
bal
l is
yel
low
”an
d B
be t
he
even
t “s
econ
d ba
ll i
s bl
ack.
”A
reth
ese
even
ts i
nd
epen
den
tor
dep
end
ent?
dep
end
ent
b.
Tel
l w
hic
h f
orm
ula
you
wou
ld u
se t
o fi
nd
the
prob
abil
ity
that
th
e fi
rst
ball
is
yell
owan
d th
e se
con
d ba
ll i
s bl
ack.
C
A.
P(Y
and
B)
�
B.P
(Yan
d B
) �
P(Y
) �
P(B
)
C.
P(Y
and
B)
�P
(Y)
�P
(Bfo
llow
ing
Y)
c.W
hic
h e
quat
ion
sh
ows
the
corr
ect
calc
ula
tion
of
this
pro
babi
lity
?B
A.
�1 3��
� 12 1��
�1 37 3�B
.�1 3�
�� 12 1�
�� 32 3�
C.
�1 3��
�1 6��
�1 2�D
.�1 3�
��1 6�
�� 11 8�
d.
Wh
ich
equ
atio
n s
how
s th
e co
rrec
t ca
lcu
lati
on o
f th
e pr
obab
ilit
y th
at i
f th
ree
ball
s ar
edr
awn
in
su
cces
sion
wit
hou
t re
plac
emen
t,al
l th
ree
wil
l be
red
?B
A.
� 15 2��
� 15 2��
� 15 2��
� 11 72 25 8�
B.�
15 2��
� 14 1��
� 13 0��
� 21 2�
C.
� 15 2��
� 14 1��
� 13 0��
�7 61 63 0�
Rem
emb
er W
hat
Yo
u L
earn
ed
2.S
ome
stu
den
ts h
ave
trou
ble
rem
embe
rin
g a
lot
of f
orm
ula
s,so
th
ey t
ry t
o ke
ep t
he
nu
mbe
r of
for
mu
las
they
hav
e to
kn
ow t
o a
min
imu
m.C
an y
ou l
earn
just
on
e fo
rmu
lath
at w
ill
allo
w y
ou t
o fi
nd
prob
abil
itie
s fo
r bo
th i
nde
pen
den
t an
d de
pen
den
t ev
ents
?E
xpla
in y
our
reas
onin
g.S
amp
le a
nsw
er:
Just
rem
emb
er t
he
form
ula
fo
rd
epen
den
t ev
ents
:P
(Aan
d B
) �
P(A
) �
P(B
follo
win
g A
).W
hen
th
eev
ents
are
ind
epen
den
t,P
(Bfo
llow
ing
A)
�P
(B),
so t
he
form
ula
fo
rd
epen
den
t ev
ents
sim
plif
ies
to P
(Aan
d B
) �
P(A
) �
P(B
),w
hic
h is
th
eco
rrec
t fo
rmu
la f
or
ind
epen
den
t ev
ents
.
P(Y
)�
�P
(Y)
�P
(B)
276
�5
Cha
pter
12
26G
lenc
oe A
lgeb
ra 2
12-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Geo
met
ric
Pro
bab
ility
If a
dar
t,th
row
n a
t ra
ndo
m,h
its
the
tria
ngu
lar
boar
d sh
own
at
the
righ
t,w
hat
is
the
chan
ce t
hat
it
wil
l h
it t
he
shad
ed r
egio
n?
Th
is
chan
ce,a
lso
call
ed a
pro
babi
lity
,can
be
dete
rmin
ed b
y co
mpa
rin
g th
e ar
ea o
f th
e sh
aded
reg
ion
to
the
area
of
the
boar
d.T
his
rat
io
indi
cate
s w
hat
fra
ctio
n o
f th
e to
sses
sh
ould
hit
in
th
e sh
aded
reg
ion
.
� ��1 22 4�
or �1 2�
In g
ener
al,i
f S
is a
su
breg
ion
of
som
e re
gion
R,t
hen
th
e pr
obab
ilit
y,P
(S),
that
a p
oin
t,ch
osen
at
ran
dom
,bel
ongs
to
subr
egio
n S
is g
iven
by
the
foll
owin
g.
P(S
) �
Fin
d t
he
pro
bab
ilit
y th
at a
poi
nt,
chos
en a
t ra
nd
om,b
elon
gs t
o th
esh
aded
su
bre
gion
s of
th
e fo
llow
ing
regi
ons.
1.�1 2�
2.�5 9�
3.�� 4�
Th
e d
art
boa
rd s
how
n a
t th
e ri
ght
has
5 c
once
ntr
ic c
ircl
es
wh
ose
cen
ters
are
als
o th
e ce
nte
r of
th
e sq
uar
e b
oard
.Eac
h
sid
e of
th
e b
oard
is
38 c
m,a
nd
th
e ra
dii
of
the
circ
les
are
2 cm
,5 c
m,8
cm
,11
cm,a
nd
14
cm.A
dar
t h
itti
ng
wit
hin
on
e of
th
e ci
rcu
lar
regi
ons
scor
es t
he
nu
mb
er o
f p
oin
ts i
nd
icat
ed
on t
he
boa
rd,w
hil
e a
hit
an
ywh
ere
else
sco
res
0 p
oin
ts.I
f a
dar
t,th
row
n a
t ra
nd
om,h
its
the
boa
rd,f
ind
th
e p
rob
abil
ity
of s
cori
ng
the
ind
icat
ed n
um
ber
of
poi
nts
.
4.0
poin
ts5.
1 po
int
6.2
poin
ts
�361 3� 61
49�
�� 17 45 4� 4
�� 15 47 4� 4
�
7.3
poin
ts8.
4 po
ints
9.5
poin
ts
� 13 49 4� 4�
� 12 41 4� 4�
� 3� 61�
51
2 34
44
4 4
46
6
64
4
33
5 5
area
of
subr
egio
n S
��
�ar
e of
reg
ion
R
�1 2� (4)
(6)
� �1 2� (8)
(6)
area
of
shad
ed r
egio
n�
��
area
of
tria
ngu
lar
boar
d
44
6
Chapter 12 A13 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 12-4)
Cha
pter
12
29G
lenc
oe A
lgeb
ra 2
Lesson 12-4
12-4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Mu
ltip
lyin
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Pro
bab
ility
of
Dep
end
ent
Even
ts
Pro
bab
ility
of T
wo
If
two
even
ts,
Aan
d B
, ar
e de
pend
ent,
then
the
pro
babi
lity
of b
oth
even
ts o
ccur
ring
isD
epen
den
t E
ven
tsP
(Aan
d B
) �
P(A
) �
P(B
follo
win
g A
).
Th
ere
are
7 d
imes
an
d 9
pen
nie
s in
a w
alle
t.S
up
pos
e tw
o co
ins
are
to b
e se
lect
ed a
t ra
nd
om,w
ith
out
rep
laci
ng
the
firs
t on
e.F
ind
th
e p
rob
abil
ity
ofp
ick
ing
a p
enn
y an
d t
hen
a d
ime.
Bec
ause
th
e co
in i
s n
ot r
epla
ced,
the
even
ts a
re d
epen
den
t.
Th
us,
P(A
and
B)
�P
(A)
�P
(Bfo
llow
ing
A).
P(p
enn
y,th
en d
ime)
�P
(pen
ny)
�P
(dim
e fo
llow
ing
pen
ny)
� 19 6��
� 17 5��
�2 81 0�
Th
e pr
obab
ilit
y is
�2 81 0�or
abo
ut
0.26
Wh
at i
s th
e p
rob
abil
ity
of d
raw
ing,
wit
hou
t re
pla
cem
ent,
3 h
eart
s,th
en a
sp
ade
from
a s
tan
dar
d d
eck
of
card
s?S
ince
th
e ca
rds
are
not
rep
lace
d,th
e ev
ents
are
dep
ende
nt.
Let
H r
epre
sen
t a
hea
rt a
nd
Sre
pres
ent
a sp
ade.
P(H
,H,H
,S)
�P
(H)
�P
(H f
ollo
win
g H
) �
P(H
fol
low
ing
2 H
s) �
P(S
fol
low
ing
3 H
s)
��1 53 2�
��1 52 1�
��1 51 0�
��1 43 9�
or a
bou
t 0.
003
Th
e pr
obab
ilit
y is
abo
ut
0.00
3 of
dra
win
g 3
hea
rts,
then
a s
pade
.
Fin
d e
ach
pro
bab
ilit
y.
1.T
he
cup
on S
oph
ie’s
des
k h
olds
4 r
ed p
ens
and
7 bl
ack
pen
s.W
hat
is
the
prob
abil
ity
ofh
er s
elec
tin
g fi
rst
a bl
ack
pen
,th
en a
red
on
e?�1 54 5�
or
abo
ut
0.25
2.W
hat
is
the
prob
abil
ity
of d
raw
ing
two
card
s sh
owin
g od
d n
um
bers
fro
m a
set
of
card
sth
at s
how
th
e fi
rst
20 c
oun
tin
g n
um
bers
if
the
firs
t ca
rd i
s n
ot r
epla
ced
befo
re t
he
seco
nd
is c
hos
en?
� 39 8�o
r ab
ou
t 0.
24
3.T
her
e ar
e 3
quar
ters
,4 d
imes
,an
d 7
nic
kels
in
a c
han
ge p
urs
e.S
upp
ose
3 co
ins
are
sele
cted
wit
hou
t re
plac
emen
t.W
hat
is
the
prob
abil
ity
of s
elec
tin
g a
quar
ter,
then
a d
ime,
and
then
a n
icke
l?� 21 6�
or
abo
ut
0.04
4.A
bas
ket
con
tain
s 4
plu
ms,
6 pe
ach
es,a
nd
5 or
ange
s.W
hat
is
the
prob
abil
ity
of p
icki
ng
2 or
ange
s,th
en a
pea
ch i
f 3
piec
es o
f fr
uit
are
sel
ecte
d at
ran
dom
?� 94 1�
or
abo
ut
0.04
5.A
ph
otog
raph
er h
as t
aken
8 b
lack
an
d w
hit
e ph
otog
raph
s an
d 10
col
or p
hot
ogra
phs
for
abr
och
ure
.If
4 ph
otog
raph
s ar
e se
lect
ed a
t ra
ndo
m,w
hat
is
the
prob
abil
ity
of p
icki
ng
firs
t2
blac
k an
d w
hit
e ph
otog
raph
s,th
en 2
col
or p
hot
ogra
phs?
� 17 02�o
r ab
ou
t 0.
07
Exam
ple
1
Exam
ple
2
Exer
cise
s
Cha
pter
12
28G
lenc
oe A
lgeb
ra 2
12-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Mu
ltip
lyin
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Pro
bab
ility
of
Ind
epen
den
t Ev
ents
Pro
bab
ility
of T
wo
If
two
even
ts,
Aan
d B
, ar
e in
depe
nden
t, th
en t
he p
roba
bilit
y of
bot
h oc
curr
ing
isIn
dep
end
ent
Eve
nts
P(A
and
B)
�P
(A)
�P
(B).
In a
boa
rd g
ame,
each
pla
yer
has
3
dif
fere
nt-
colo
red
mar
ker
s.T
o m
ove
arou
nd
th
e b
oard
,th
e p
laye
r fi
rst
spin
s a
spin
ner
to
det
erm
ine
wh
ich
pie
ce c
an b
e m
oved
.He
or s
he
then
rol
ls a
die
to
det
erm
ine
how
man
y sp
aces
that
col
ored
pie
ce s
hou
ld m
ove.
On
a g
iven
tu
rn,w
hat
is
the
pro
bab
ilit
y th
at a
pla
yer
wil
l b
e ab
le t
o m
ove
the
yell
ow p
iece
m
ore
than
2 s
pac
es?
Let
Abe
th
e ev
ent
that
th
e sp
inn
er l
ands
on
yel
low
,an
d le
t B
be t
he
even
t th
at t
he
die
show
s a
nu
mbe
r gr
eate
r th
an 2
.Th
e pr
obab
ilit
y of
Ais
�1 3� ,an
d th
e pr
obab
ilit
y of
Bis
�2 3� .
P(A
and
B)
�P
(A)
�P
(B)
Pro
babi
lity
of in
depe
nden
t ev
ents
��1 3�
��2 3�
or �2 9�
Sub
stitu
te a
nd m
ultip
ly.
Th
e pr
obab
ilit
y th
at t
he
play
er c
an m
ove
the
yell
ow p
iece
mor
e th
an 2
spa
ces
is �2 9� .
A d
ie i
s ro
lled
3 t
imes
.Fin
d t
he
pro
bab
ilit
y of
eac
h e
ven
t.
1.a
1 is
rol
led,
then
a 2
,th
en a
3� 21 16�
2.a
1 or
a 2
is
roll
ed,t
hen
a 3
,th
en a
5 o
r a
6� 51 4�
3.2
odd
nu
mbe
rs a
re r
olle
d,th
en a
6� 21 4�
4.a
nu
mbe
r le
ss t
han
3 i
s ro
lled
,th
en a
3,t
hen
a n
um
ber
grea
ter
than
3� 31 6�
5.A
box
con
tain
s 5
tria
ngl
es,6
cir
cles
,an
d 4
squ
ares
.If
a fi
gure
is
rem
oved
,rep
lace
d,an
da
seco
nd
figu
re i
s pi
cked
,wh
at i
s th
e pr
obab
ilit
y th
at a
tri
angl
e an
d th
en a
cir
cle
wil
l be
pic
ked?
� 12 5�o
r ab
ou
t 0.
13
6.A
bag
con
tain
s 5
red
mar
bles
an
d 4
wh
ite
mar
bles
.A m
arbl
e is
sel
ecte
d fr
om t
he
bag,
then
rep
lace
d,an
d a
seco
nd
sele
ctio
n i
s m
ade.
Wh
at i
s th
e pr
obab
ilit
y of
sel
ecti
ng
2 re
dm
arbl
es?
�2 85 1�o
r ab
ou
t 0.
31
7.A
jar
con
tain
s 7
lem
on ja
wbr
eake
rs,3
ch
erry
jaw
brea
kers
,an
d 8
rain
bow
jaw
brea
kers
.W
hat
is
the
prob
abil
ity
of s
elec
tin
g 2
lem
on ja
wbr
eake
rs i
n s
ucc
essi
on p
rovi
din
g th
eja
wbr
eake
r dr
awn
fir
st i
s th
en r
epla
ced
befo
re t
he
seco
nd
is d
raw
n?
� 34 29 4�o
r ab
ou
t0.1
5
blue
red
yello
w
Exam
ple
Exer
cise
s
Chapter 12 A14 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 12-4)
Cha
pter
12
31G
lenc
oe A
lgeb
ra 2
Lesson 12-4
12-4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Prac
tice
Mu
ltip
lyin
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
A d
ie i
s ro
lled
th
ree
tim
es.F
ind
eac
h p
rob
abil
ity.
1.P
(th
ree
4s)
� 21 16�2.
P(n
o 4s
)�1 22 15 6�
3.P
(2,t
hen
3,t
hen
1)
� 21 16�4.
P(t
hre
e di
ffer
ent
even
nu
mbe
rs)
� 31 6�
5.P
(an
y n
um
ber,
then
5,t
hen
5)
� 31 6�6.
P(e
ven
nu
mbe
r,th
en o
dd n
um
ber,
then
1)
� 21 4�
Th
ere
are
3 n
ick
els,
2 d
imes
,an
d 5
qu
arte
rs i
n a
pu
rse.
Th
ree
coin
s ar
e se
lect
ed i
nsu
cces
sion
at
ran
dom
.Fin
d t
he
pro
bab
ilit
y.
7.P
(nic
kel,
then
dim
e,th
en q
uar
ter)
,if
no
repl
acem
ent
occu
rs� 21 4�
8.P
(nic
kel,
then
dim
e,th
en q
uar
ter)
,if
repl
acem
ent
occu
rs� 13 00�
9.P
(2 n
icke
ls,t
hen
1 q
uar
ter)
,if
no
repl
acem
ent
occu
rs� 21 4�
10.P
(3 d
imes
),if
rep
lace
men
t oc
curs
� 11 25�
11.P
(3 d
imes
),if
no
repl
acem
ent
occu
rs0
For
Exe
rcis
es 1
2 an
d 1
3,d
eter
min
e w
het
her
th
e ev
ents
are
in
dep
end
ent
ord
epen
den
t.T
hen
fin
d e
ach
pro
bab
ilit
y.
12.S
eren
a is
cre
atin
g a
pain
ting
.She
wan
ts t
o us
e 2
mor
e co
lors
.She
cho
oses
ran
dom
ly f
rom
6 sh
ades
of
red,
10 s
had
es o
f gr
een
,4 s
had
es o
f ye
llow
,4 s
had
es o
f pu
rple
,an
d 6
shad
esof
blu
e.W
hat
is
the
prob
abil
ity
that
sh
e ch
oose
s 2
shad
es o
f gr
een
?d
epen
den
t;� 23 9�
13.K
ersh
el’s
mot
her
is
shop
pin
g at
a b
aker
y.T
he
own
er o
ffer
s K
ersh
el a
coo
kie
from
a ja
rco
nta
inin
g 22
ch
ocol
ate
chip
coo
kies
,18
suga
r co
okie
s,an
d 15
oat
mea
l co
okie
s.W
ith
out
look
ing,
Ker
shel
sel
ects
on
e,dr
ops
it b
ack
in,a
nd
then
ran
dom
ly s
elec
ts a
not
her
.Wh
at i
sth
e pr
obab
ilit
y th
at n
eith
er s
elec
tion
was
a c
hoc
olat
e ch
ip c
ooki
e?in
dep
end
ent;
� 29 5�
14.M
ETEO
RO
LOG
YT
he
Fade
eva’
s ar
e pl
ann
ing
a 3-
day
vaca
tion
to
the
mou
nta
ins.
Alo
ng-
ran
ge f
orec
ast
repo
rts
that
th
e pr
obab
ilit
y of
rai
n e
ach
day
is
10%
.Ass
um
ing
that
the
dail
y pr
obab
ilit
ies
of r
ain
are
in
depe
nde
nt,
wh
at i
s th
e pr
obab
ilit
y th
at t
her
e is
no
rain
on
th
e fi
rst
two
days
,bu
t th
at i
t ra
ins
on t
he
thir
d da
y?� 18 01 00�
RA
ND
OM
NU
MB
ERS
For
Exe
rcis
es 1
5 an
d 1
6,u
se t
he
foll
owin
g in
form
atio
n.
An
ita
has
a l
ist
of 2
0 jo
bs a
rou
nd
the
hou
se t
o do
,an
d pl
ans
to d
o 3
of t
hem
tod
ay.S
he
assi
gns
each
job
a n
um
ber
from
1 t
o 20
,an
dse
ts h
er c
alcu
lato
r to
gen
erat
e ra
ndo
m n
um
bers
fro
m 1
to
20,w
hic
hca
n r
eocc
ur.
Of
the
jobs
,3 a
re o
uts
ide,
and
the
rest
are
in
side
.
15.S
ketc
h a
tre
e di
agra
m s
how
ing
all
of t
he
poss
ibil
itie
s th
at t
he
firs
t th
ree
nu
mbe
rs g
ener
ated
cor
resp
ond
to
insi
de jo
bs o
r ou
tsid
e jo
bs.U
se i
t to
fin
d th
e pr
obab
ilit
y th
at t
he
firs
t tw
o n
um
bers
cor
resp
ond
to i
nsi
de jo
bs,
and
the
thir
d to
an
ou
tsid
e jo
b.0.
1083
75
16.W
hat
is
the
prob
abil
ity
that
th
e n
um
ber
gen
erat
ed
corr
espo
nds
to
an o
uts
ide
job
thre
e ti
mes
in
a r
ow?
0.00
3375
I O
0.85
0.15
I O
0.85
0.15
I O
0.85
0.15
I O
0.85
0.15
I O
0.85
0.15
I O
0.85
0.15
I O
0.85
0.15
Cha
pter
12
30G
lenc
oe A
lgeb
ra 2
12-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceM
ult
iply
ing
Pro
bab
iliti
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
A d
ie i
s ro
lled
tw
ice.
Fin
d e
ach
pro
bab
ilit
y.
1.P
(5,t
hen
6)
� 31 6�2.
P(n
o 2s
)�2 35 6�
3.P
(tw
o 1s
)� 31 6�
4.P
(an
y n
um
ber,
then
not
5)
�5 6�5.
P(4
,th
en n
ot 6
)� 35 6�
6.P
(not
1,t
hen
not
2)
�2 35 6�
A b
oard
gam
e u
ses
a se
t of
6 d
iffe
ren
t ca
rds.
Eac
h c
ard
dis
pla
ys o
ne
of t
he
foll
owin
gfi
gure
s:a
star
,a s
qu
are,
a ci
rcle
,a d
iam
ond
,a r
ecta
ngl
e,or
a p
enta
gon
.Th
e ca
rds
are
pla
ced
fac
e d
own
,an
d a
pla
yer
choo
ses
two
card
s.F
ind
eac
h p
rob
abil
ity.
7.P
(cir
cle,
then
sta
r),i
f n
o re
plac
emen
t oc
curs
� 31 0�
8.P
(dia
mon
d,th
en s
quar
e),i
f re
plac
emen
t oc
curs
� 31 6�
9.P
(2 p
olyg
ons)
,if
repl
acem
ent
occu
rs�2 35 6�
10.P
(2 p
olyg
ons)
,if
no
repl
acem
ent
occu
rs�2 3�
11.P
(cir
cle,
then
hex
agon
),if
no
repl
acem
ent
occu
rs0
Det
erm
ine
wh
eth
er t
he
even
ts a
re i
nd
epen
den
tor
dep
end
ent.
Th
en f
ind
eac
hp
rob
abil
ity.
12.A
mix
ed b
ox o
f h
erba
l te
abag
s co
nta
ins
2 le
mon
tea
bags
,3 o
ran
ge-m
ango
tea
bags
,3
cham
omil
e te
abag
s,an
d 1
apri
cot-
gin
ger
teab
ag.K
evin
ch
oose
s 2
teab
ags
at r
ando
m t
obr
ing
to w
ork
wit
h h
im.W
hat
is
the
prob
abil
ity
that
he
firs
t ch
oose
s a
lem
on t
eaba
g an
dth
en a
ch
amom
ile
teab
ag?
dep
end
ent;
� 11 2�
13.T
he
char
t sh
ows
the
sele
ctio
n o
f ol
ive
oils
th
at
Has
ha
fin
ds i
n a
spe
cial
ty f
oods
cat
alog
.If
she
ran
dom
ly s
elec
ts o
ne
type
of
oil,
then
ran
dom
lyse
lect
s an
oth
er,d
iffe
ren
t oi
l,w
hat
is
the
prob
abil
ity
that
bot
h s
elec
tion
s ar
e do
mes
tic,
firs
t co
ld p
ress
ed o
ils?
dep
end
ent;
� 82 21 0�
For
Exe
rcis
es 1
4 an
d 1
5,tw
o th
ird
s of
th
e ar
ea o
f th
e sp
inn
er
earn
s yo
u 5
0 p
oin
ts.S
up
pos
e yo
u s
pin
th
e sp
inn
er t
wic
e.
14.S
ketc
h a
tre
e di
agra
m s
how
ing
all
of t
he
poss
ibil
itie
s.U
se i
t to
fin
d th
e pr
obab
ilit
y of
spin
nin
g 50
poi
nts
,th
en 1
00 p
oin
ts.
�2 9�
15.W
hat
is
the
prob
abil
ity
that
you
get
100
poi
nts
on
eac
h s
pin
?�1 9�
50 100
50 100
2 3
50 100
2 3 2 31 3
1 31 3
100
50
Typ
e o
f O
ilD
om
esti
cIm
po
rted
Pur
e2
5
Col
d P
ress
ed4
8
Firs
t C
old
Pre
ssed
715
Chapter 12 A15 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 12-4)
Cha
pter
12
33G
lenc
oe A
lgeb
ra 2
Lesson 12-4
12-4
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Co
nd
itio
nal
Pro
bab
ility
Su
ppos
e a
pair
of
dice
is
thro
wn
.It
is k
now
n t
hat
th
e su
m i
s gr
eate
r th
anse
ven
.Fin
d th
e pr
obab
ilit
y th
at t
he
dice
mat
ch.
Th
e pr
obab
ilit
y of
an
eve
nt
give
n t
he
occu
rren
ce o
f an
oth
er e
ven
t is
cal
led
con
dit
ion
al p
roba
bili
ty.T
he
con
diti
onal
pro
babi
lity
of
even
t A
,th
e di
cem
atch
,giv
en e
ven
t B
,th
eir
sum
is
grea
ter
than
sev
en,i
s de
not
ed P
(A/B
).
Th
ere
are
15 s
um
s gr
eate
r th
an s
even
an
dth
ere
are
36 p
ossi
ble
pair
s al
toge
ther
.
P(B
) �
�1 35 6�
Th
ere
are
thre
e m
atch
ing
pair
s gr
eate
rth
an s
even
.
P(A
and
B)
�� 33 6�
P(A
/B)
�
P(A
/B)
�or
�1 5�
Th
e co
ndi
tion
al p
roba
bili
ty i
s �1 5� .
A c
ard
is
dra
wn
fro
m a
sta
nd
ard
dec
k o
f 52
an
d i
s fo
un
d t
o b
e re
d.
Giv
en t
hat
eve
nt,
fin
d e
ach
of
the
foll
owin
g p
rob
abil
itie
s.
1.P
(hea
rt)
�1 2�2.
P(a
ce)
� 11 3�3.
P(f
ace
card
)� 13 3�
4.P
(jac
k or
ten
)� 12 3�
5.P
(six
of
spad
es)
06.
P(s
ix o
f h
eart
s)� 21 6�
A s
por
ts s
urv
ey t
aken
at
Sti
rers
Hig
h S
choo
l sh
ows
that
48%
of
the
resp
ond
ents
lik
ed s
occe
r,66
% l
iked
bas
ket
bal
l,an
d 3
8% l
iked
hoc
key
.A
lso,
30%
lik
ed s
occe
r an
d b
ask
etb
all,
22%
lik
ed b
ask
etb
all
and
hoc
key
and
28%
lik
ed s
occe
r an
d h
ock
ey.F
inal
ly,1
2% l
iked
all
th
ree
spor
ts.
Fin
d e
ach
of
the
foll
owin
g p
rob
abil
itie
s.
7.T
he
prob
abil
ity
Meg
lik
es s
occe
r if
sh
e li
kes
bask
etba
ll.
�3 60 6�o
r � 15 1�
8.T
he
prob
abil
ity
Bif
f li
kes
bask
etba
ll i
f h
e li
kes
socc
er.
�3 40 8�o
r �5 8�
9.T
he
prob
abil
ity
Mu
ffy
like
s h
ocke
y if
sh
e li
kes
bask
etba
ll.
�2 62 6�o
r �1 3�
10.T
he
prob
abil
ity
Gre
g li
kes
hoc
key
and
bask
etba
ll i
f h
e li
kes
socc
er.
�1 42 8�o
r �1 4�
� 33 6�
� �1 35 6�P(A
and
B)
��
P(B
)
Cha
pter
12
32G
lenc
oe A
lgeb
ra 2
12-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Mu
ltip
lyin
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1.B
USS
ING
Por
tia
and
Qu
into
n u
se
the
sam
e bu
s st
op w
hen
th
ey g
o to
w
ork.
Th
ey a
rriv
e at
th
e bu
s st
opin
depe
nde
ntl
y of
eac
h o
ther
.Th
epr
obab
ilit
y th
at P
orti
a ca
tch
es t
he
7:45
A.M
.bu
s is
.T
he
prob
abil
ity
that
Qu
into
n c
atch
es t
he
7:45
A.M
.bu
s is
.
Wh
at i
s th
e pr
obab
ilit
y th
at t
hey
bot
hca
tch
th
e 7:
45 A
.M.b
us
on t
he
sam
e da
y?
2.G
OO
DY
BA
GS
Rya
n a
nd
Sop
hia
are
give
n g
oody
bag
s w
ith
ide
nti
cal
con
ten
ts.
Th
e pr
obab
ilit
y of
rea
chin
g in
to e
ith
er
of t
hes
e go
ody
bags
an
d pu
llin
g ou
t a
stic
k of
ch
ewin
g gu
m i
s .R
yan
an
d
Sop
hia
eac
h r
each
in
to t
hei
r ow
n g
oody
bag
and
ran
dom
ly p
ull
ou
t so
met
hin
g.W
hat
is
the
prob
abil
ity
that
th
ey b
oth
pull
ed o
ut
a st
ick
of c
hew
ing
gum
?
3.PE
NC
ILS
A b
ox o
f pe
nci
ls c
onta
ins
11 t
ype
2 pe
nci
ls a
nd
5 ty
pe 3
pen
cils
.T
ara
pick
s ou
t a
pen
cil
from
th
e bo
xw
ith
out
look
ing
and
keep
s it
.Th
en,
Upt
on p
icks
ou
t a
pen
cil
from
th
e bo
xw
ith
out
look
ing.
Wh
at i
s th
e pr
obab
ilit
yth
at T
ara
pick
s a
type
2 p
enci
l an
dU
pton
pic
ks a
typ
e 3
pen
cil?
11 � 481� 10
0
1 � 10
3 � 10
1 � 2
3 � 5
4.G
UES
SIN
G G
AM
ESV
aler
ie i
s pl
ayin
ga
gues
sin
g ga
me.
Fou
r ca
rds
are
plac
edfa
ce d
own
bef
ore
her
.Th
e h
idde
n s
ide
ofea
ch c
ard
show
s ei
ther
th
e w
ord
“LO
SE
”or
“W
IN”.
On
ly o
ne
card
is
labe
led
“WIN
”.V
aler
ie i
s gi
ven
tw
o ch
ance
s to
fin
d th
e ca
rd l
abel
ed “
WIN
”.
Wh
at i
s th
e pr
obab
ilit
y th
at s
he
does
n
ot p
ick
the
“win
”ca
rd o
n h
er f
irst
try
but
does
fin
d it
wit
h h
er s
econ
d?
WA
LLET
SF
or E
xerc
ises
5 a
nd
6,u
seth
e fo
llow
ing
info
rmat
ion
.
Way
ne
has
1 t
en-d
olla
r bi
ll,2
fiv
e-do
llar
bill
s,an
d 5
one-
doll
ar b
ills
in
his
wal
let.
5.W
ayn
e ra
ndo
mly
ch
oose
s a
bill
fro
m h
isw
alle
t,pu
ts i
t ba
ck,t
hen
pic
ks a
not
her
bill
,an
d pu
ts t
hat
on
e ba
ck,t
oo.W
hat
is
the
prob
abil
ity
that
bot
h w
ere
five
-dol
lar
bill
s?
6.W
ayn
e ra
ndo
mly
pu
lls
out
a bi
ll f
rom
h
is w
alle
t,an
d th
en,w
ith
out
putt
ing
itba
ck,r
ando
mly
pu
lls
a se
con
d bi
ll f
rom
his
wal
let.
He
then
pu
ts b
oth
bil
ls b
ack
into
th
e w
alle
t.W
hat
is
the
prob
abil
ity
that
bot
h o
f th
e bi
lls
pull
ed o
ut
wer
efi
ve-d
olla
r bi
lls?
1 � 281 � 161 � 4
WIN
LOSE
Chapter 12 A16 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 12-5)
Cha
pter
12
35G
lenc
oe A
lgeb
ra 2
Lesson 12-5
12-5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Ad
din
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Mu
tual
ly E
xclu
sive
Eve
nts
Eve
nts
th
at c
ann
ot o
ccu
r at
th
e sa
me
tim
e ar
e ca
lled
mu
tual
ly e
xclu
sive
eve
nts
.
Pro
bab
ility
of
Mu
tual
ly
If tw
o ev
ents
, A
and
B,
are
mut
ually
exc
lusi
ve,
then
Exc
lusi
ve E
ven
tsP
(Aor
B)
�P
(A)
�P
(B).
Th
is f
orm
ula
can
be
exte
nde
d to
an
y n
um
ber
of m
utu
ally
exc
lusi
ve e
ven
ts.
To
choo
se a
n a
fter
noo
n a
ctiv
ity,
sum
mer
cam
per
s p
ull
sli
ps
ofp
aper
ou
t of
a h
at.T
oday
th
ere
are
25 s
lip
s fo
r a
nat
ure
wal
k,3
5 sl
ips
for
swim
min
g,an
d 3
0 sl
ips
for
arts
an
d c
raft
s.W
hat
is
the
pro
bab
ilit
y th
at a
cam
per
wil
l p
ull
a s
lip
for
a n
atu
re w
alk
or
for
swim
min
g?T
hes
e ar
e m
utu
ally
exc
lusi
ve e
ven
ts.N
ote
that
th
ere
is a
tot
al o
f 90
sli
ps.
P(n
atu
re w
alk
or s
wim
min
g) �
P(n
atu
re w
alk)
�P
(sw
imm
ing)
��2 95 0�
��3 95 0�
or �2 3�
Th
e pr
obab
ilit
y of
a c
ampe
r’s
pull
ing
out
a sl
ip f
or a
nat
ure
wal
k or
for
sw
imm
ing
is �2 3� .
By
the
tim
e on
e te
nt
of 6
cam
per
s ge
ts t
o th
e fr
ont
of t
he
lin
e,th
ere
are
only
10
nat
ure
wal
k s
lip
s an
d 1
5 sw
imm
ing
slip
s le
ft.W
hat
is
the
pro
bab
ilit
yth
at m
ore
than
4 o
f th
e 6
cam
per
s w
ill
choo
se a
sw
imm
ing
slip
?
P(m
ore
than
4 s
wim
mer
s) �
P(5
sw
imm
ers)
�P
(6 s
wim
mer
s)
��
�0.
2T
he
prob
abil
ity
of m
ore
than
4 o
f th
e ca
mpe
rs s
wim
min
g is
abo
ut
0.2.
Fin
d e
ach
pro
bab
ilit
y.
1.A
bag
con
tain
s 45
dye
d eg
gs:1
5 ye
llow
,12
gree
n,a
nd
18 r
ed.W
hat
is
the
prob
abil
ity
ofse
lect
ing
a gr
een
or
a re
d eg
g?�2 3�
2.T
he
lett
ers
from
th
e w
ords
LO
VE
an
d L
IVE
are
pla
ced
on c
ards
an
d pu
t in
a b
ox.W
hat
is t
he
prob
abil
ity
of s
elec
tin
g an
L o
r an
O f
rom
th
e bo
x?�3 8�
3.A
pai
r of
dic
e is
rol
led,
and
the
two
nu
mbe
rs a
re a
dded
.Wh
at i
s th
e pr
obab
ilit
y th
at t
he
sum
is
eith
er a
5 o
r a
7?� 15 8�
or
abo
ut
0.28
4.A
bow
l h
as 1
0 w
hol
e w
hea
t cr
acke
rs,1
6 se
sam
e cr
acke
rs,a
nd
14 r
ye c
risp
s.If
a p
erso
npi
cks
a cr
acke
r at
ran
dom
,wh
at i
s th
e pr
obab
ilit
y of
pic
kin
g ei
ther
a s
esam
e cr
acke
r or
a ry
e cr
isp?
�3 4�
5.A
n ar
t bo
x co
ntai
ns 1
2 co
lore
d pe
ncil
s an
d 20
pas
tels
.If
5 dr
awin
g im
plem
ents
are
cho
sen
at r
ando
m,w
hat
is
the
prob
abil
ity
that
at
leas
t 4
of t
hem
are
pas
tels
?ab
ou
t 0.
37
C(1
0,0)
�C
(15,
6)�
��
C(2
5,6)
C(1
0,1)
�C
(15,
5)�
��
C(2
5,6)
Exam
ple
1
Exam
ple
2
Exer
cise
s
Cha
pter
12
34G
lenc
oe A
lgeb
ra 2
12-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Ad
din
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
2-5
in y
our
text
boo
k.
Wh
y do
th
e pe
rcen
tage
s sh
own
on
th
e ba
r gr
aph
add
up
to m
ore
than
100
%?
Sam
ple
answ
er:
Man
y te
ens
do
on
e o
r m
ore
of
the
liste
d o
nlin
e ac
tivi
ties
.
Rea
d t
he
Less
on
1.In
dica
te w
het
her
th
e ev
ents
in
eac
h p
air
are
incl
usi
veor
mu
tual
ly e
xclu
sive
.
a.Q
:dra
win
g a
quee
n f
rom
a s
tan
dard
dec
k of
car
dsD
:dra
win
g a
diam
ond
from
a s
tan
dard
dec
k of
car
dsin
clu
sive
b.
J:d
raw
ing
a ja
ck f
rom
a s
tan
dard
dec
k of
car
dsK
:dra
win
g a
kin
g fr
om a
sta
nda
rd d
eck
of c
ards
mu
tual
ly e
xclu
sive
2.M
arla
too
k a
quiz
on
th
is l
esso
n t
hat
con
tain
ed t
he
foll
owin
g pr
oble
m.
Eac
h o
f th
e in
tege
rs f
rom
1 t
hro
ugh
25
is w
ritt
en o
n a
sli
p of
pap
er a
nd
plac
ed i
n a
nen
velo
pe.I
f on
e sl
ip i
s dr
awn
at
ran
dom
,wh
at i
s th
e pr
obab
ilit
y th
at i
t is
odd
or
am
ult
iple
of
5?H
ere
is M
arla
’s w
ork.
P(o
dd)
��1 23 5�
P(m
ult
iple
of
5) �
� 25 5�or
�1 5�
P(o
dd o
r m
ult
iple
of
5) �
P(o
dd)
�P
(mu
ltip
le o
f 5)
��1 23 5�
�� 25 5�
��1 28 5�
a.W
hy
is M
arla
’s w
ork
inco
rrec
t?S
amp
le a
nsw
er:
Mar
la u
sed
th
e fo
rmu
la f
or
mu
tual
ly e
xclu
sive
eve
nts
,bu
t th
e ev
ents
are
incl
usi
ve.S
he
sho
uld
use
th
e fo
rmu
la f
or
incl
usi
ve e
ven
ts s
o t
hat
th
e o
dd
mu
ltip
les
of
5 w
illn
ot
be
cou
nte
d t
wic
e.
b.
Sh
ow t
he
corr
ecte
d w
ork.
P(o
dd o
r m
ultip
le o
f 5)
�P
(odd
) �
P(m
ultip
le o
f 5)
�P
(odd
mul
tiple
of
5)
��1 23 5�
�� 25 5�
�� 23 5�
��1 25 5�
��3 5�
Rem
emb
er W
hat
Yo
u L
earn
ed
3.S
ome
stu
den
ts h
ave
trou
ble
rem
embe
rin
g a
lot
of f
orm
ula
s,so
th
ey t
ry t
o ke
ep t
he
nu
mbe
r of
for
mu
las
they
hav
e to
kn
ow t
o a
min
imu
m.C
an y
ou l
earn
just
on
e fo
rmu
lath
at w
ill
allo
w y
ou t
o fi
nd
prob
abil
itie
s fo
r bo
th m
utu
ally
exc
lusi
ve a
nd
incl
usi
ve e
ven
ts?
Exp
lain
you
r re
ason
ing.
Sam
ple
an
swer
:Ju
st r
emem
ber
th
e fo
rmu
la f
or
incl
usi
ve e
ven
ts:
P(A
or
B)
�P
(A)
�P
(B)
�P
(Aan
d B
).W
hen
th
eev
ents
are
mu
tual
ly e
xclu
sive
,P(A
and
B)
�0,
so t
he
form
ula
fo
rin
clu
sive
eve
nts
sim
plif
ies
to P
(Aan
d B
) �
P(A
) �
P(B
),w
hic
h is
th
eco
rrec
t fo
rmu
la f
or
mu
tual
ly e
xclu
sive
eve
nts
.
Chapter 12 A17 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 12-5)
Cha
pter
12
37G
lenc
oe A
lgeb
ra 2
Lesson 12-5
12-5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceA
dd
ing
Pro
bab
iliti
es
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Eli
has
10
bas
ebal
l ca
rds
of 1
0 d
iffe
ren
t p
laye
rs i
n h
is p
ock
et.T
hre
e p
laye
rs a
rep
itch
ers,
5 ar
e ou
tfie
lder
s,an
d 2
are
cat
cher
s.If
Eli
ran
dom
ly s
elec
ts a
car
d t
otr
ade,
fin
d e
ach
pro
bab
ilit
y.
1.P
(pit
cher
or
outf
ield
er)
�4 5�2.
P(p
itch
er o
r ca
tch
er)
�1 2�3.
P(o
utf
ield
er o
r ca
tch
er)
� 17 0�
A d
ie i
s ro
lled
.Fin
d e
ach
pro
bab
ilit
y.
4.P
(5 o
r 6)
�1 3�5.
P(a
t le
ast
a 3)
�2 3�6.
P(l
ess
than
4)
�1 2�
Det
erm
ine
wh
eth
er t
he
even
ts a
re m
utu
all
y ex
clu
sive
or i
ncl
usi
ve.T
hen
fin
d t
he
pro
bab
ilit
y.
7.A
die
is
roll
ed.W
hat
is
the
prob
abil
ity
of r
olli
ng
a 3
or a
4?
mu
tual
ly e
xclu
sive
;�1 3�
8.A
die
is
roll
ed.W
hat
is
the
prob
abil
ity
of r
olli
ng
an e
ven
nu
mbe
r or
a 4
?in
clu
sive
;�1 2�
9.A
car
d is
dra
wn
fro
m a
sta
nda
rd d
eck
of c
ards
.Wh
at i
s th
e pr
obab
ilit
y of
dra
win
g a
kin
gor
a q
uee
n?
mu
tual
ly e
xclu
sive
;� 12 3�
10.A
car
d is
dra
wn
fro
m a
sta
nda
rd d
eck
of c
ards
.Wh
at i
s th
e pr
obab
ilit
y of
dra
win
g a
jack
or a
hea
rt?
incl
usi
ve;
� 14 3�
11.T
he
soph
omor
e cl
ass
is s
elli
ng
Mot
her
’s D
ay p
lan
ts t
o ra
ise
mon
ey.S
usa
n’s
pri
ze f
orbe
ing
the
top
sell
er o
f pl
ants
is
a ch
oice
of
a bo
ok,a
CD
,or
a vi
deo.
Sh
e ca
n c
hoo
se f
rom
6 bo
oks,
3 C
Ds,
and
5 vi
deos
.Wh
at i
s th
e pr
obab
ilit
y th
at S
usa
n s
elec
ts a
boo
k or
a C
D?
mu
tual
ly e
xclu
sive
;� 19 4�
A s
pin
ner
nu
mb
ered
1�
10 i
s sp
un
.Fin
d e
ach
pro
bab
ilit
y.
12.P
(les
s th
an 5
or
even
)� 17 0�
13.P
(eve
n o
r od
d)1
14.P
(pri
me
or e
ven
)�4 5�
Tw
o ca
rds
are
dra
wn
fro
m a
sta
nd
ard
dec
k o
f ca
rds.
Fin
d e
ach
pro
bab
ilit
y.
15.P
(bot
h r
ed o
r bo
th b
lack
)�2 55 1�
16.P
(bot
h a
ces
or b
oth
red
)� 25 25 1�
17.P
(bot
h 2
s or
bot
h l
ess
than
5)
� 21 21 1�18
.P(b
oth
bla
ck o
r bo
th l
ess
than
5)
�1 68 68 3�
For
Exe
rcis
es 1
9 an
d 2
0,u
se t
he
Ven
n d
iagr
am t
hat
sh
ows
the
nu
mb
er o
f p
arti
cip
ants
in
tw
o d
iffe
ren
t k
ind
s of
aer
obic
exe
rcis
e cl
asse
s th
at a
re o
ffer
ed a
t a
hea
lth
clu
b.
Det
erm
ine
each
pro
bab
ilit
y if
a p
erso
n
is s
elec
ted
at
ran
dom
fro
m t
he
par
tici
pan
ts.
19.P
(ste
p ae
robi
cs o
r ja
zzer
cise
,bu
t n
ot b
oth
)�4 69 2�
20.P
(ste
p ae
robi
cs a
nd
jazz
erci
se)
�1 63 2�
Jazz
erci
seS
tep
Aer
ob
ics
2722
13
Cha
pter
12
36G
lenc
oe A
lgeb
ra 2
12-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Ad
din
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Incl
usi
ve E
ven
ts
Pro
bab
ility
of
Incl
usi
ve E
ven
tsIf
two
even
ts,
Aan
d B
, ar
e in
clus
ive,
P(A
or B
) �
P(A
) �
P(B
) �
P(A
and
B).
Wh
at i
s th
e p
rob
abil
ity
of d
raw
ing
a fa
ce c
ard
or
a b
lack
car
d f
rom
a st
and
ard
dec
k o
f ca
rds?
Th
e tw
o ev
ents
are
in
clu
sive
,sin
ce a
car
d ca
n b
e bo
th a
fac
e ca
rd a
nd
a bl
ack
card
.
P(f
ace
card
or
blac
k ca
rd)
�P
(fac
e ca
rd)
�P
(bla
ck c
ard)
�P
(bla
ck f
ace
card
)
�� 13 3�
��1 2�
�� 23 6�
�� 18 3�
or a
bou
t 0.
62
Th
e pr
obab
ilit
y of
dra
win
g ei
ther
a f
ace
card
or
a bl
ack
card
is
abou
t 0.
62
Fin
d e
ach
pro
bab
ilit
y.
1.W
hat
is
the
prob
abil
ity
of d
raw
ing
a re
d ca
rd o
r an
ace
fro
m a
sta
nda
rd d
eck
of c
ards
?
� 17 3�o
r ab
ou
t 0.
54
2.T
hre
e ca
rds
are
sele
cted
fro
m a
sta
nda
rd d
eck
of 5
2 ca
rds.
Wh
at i
s th
e pr
obab
ilit
y of
sele
ctin
g a
kin
g,a
quee
n,o
r a
red
card
?
�1 25 6�o
r ab
ou
t 0.
58
3.T
he
lett
ers
of t
he
alph
abet
are
pla
ced
in a
bag
.Wh
at i
s th
e pr
obab
ilit
y of
sel
ecti
ng
avo
wel
or
one
of t
he
lett
ers
from
th
e w
ord
QU
IZ?
� 27 6�o
r ab
ou
t 0.
27
4.A
pai
r of
dic
e is
rol
led.
Wh
at i
s th
e pr
obab
ilit
y th
at t
he
sum
is
odd
or a
mu
ltip
le o
f 3?
�2 3�o
r ab
ou
t 0.
67
5.T
he
Ven
n d
iagr
am a
t th
e ri
ght
show
s th
e n
um
ber
of
ju
nio
rs o
n v
arsi
ty s
port
s te
ams
at E
lmw
ood
Hig
h S
choo
l.S
ome
ath
lete
s ar
e on
var
sity
tea
ms
for
one
seas
on o
nly
,so
me
ath
lete
s fo
r tw
o se
ason
s,an
d so
me
for
all
thre
ese
ason
s.If
a v
arsi
ty a
thle
te i
s ch
osen
at
ran
dom
fro
m
the
jun
ior
clas
s,w
hat
is
the
prob
abil
ity
that
he
or s
he
play
s a
fall
or
win
ter
spor
t?�1 13 6�
Win
ter
Jun
iors
Pla
yin
g V
arsi
ty S
po
rts
Sp
rin
g
Fall
5
6
83 5
41
Exam
ple
Exer
cise
s
Chapter 12 A18 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 12-5)
Cha
pter
12
39G
lenc
oe A
lgeb
ra 2
Lesson 12-5
12-5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Ad
din
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1.PI
CK
-UP
Wh
en T
ina’
s pa
ren
ts p
ick
her
up
from
sch
ool,
ther
e is
a
chan
ce t
hat
she
wil
l be
in
th
e li
brar
y,a
chan
ce
that
sh
e w
ill
be o
n t
he
play
grou
nd,
and
a ch
ance
th
at s
he
wil
l be
in
her
clas
sroo
m.W
hat
is
the
prob
abil
ity
that
wh
en T
ina’
s pa
ren
ts p
ick
her
up,
she
is f
oun
d in
her
cla
ssro
om o
r on
th
epl
aygr
oun
d?
2.TR
AV
ELJo
hn
is
ran
dom
ly s
elec
ted
to b
e gi
ven
a c
han
ce t
o w
in a
new
car
.H
e m
ust
ch
oose
a r
ed o
r ye
llow
mar
ble
from
a b
ag c
onta
inin
g 1
red,
2 ye
llow
,10
gre
en,a
nd
12 b
lue
mar
bles
.Wh
at i
sth
e pr
obab
ilit
y h
e w
ill
win
th
e ca
r?
3.D
ICE
Ale
xis
roll
s tw
o id
enti
cal
dice
.W
hat
is
the
prob
abil
ity
that
th
e su
m
of t
he
nu
mbe
rs r
olle
d is
odd
? W
hat
is
th
e pr
obab
ilit
y th
at t
he
sum
of
the
nu
mbe
rs r
olle
d is
gre
ater
th
an 7
? W
hat
is t
he
prob
abil
ity
that
th
e su
m o
f th
en
um
bers
rol
led
is o
dd o
r gr
eate
r th
an 7
?
P(o
dd
) �
;P
(7)
�;
P(o
dd
or
7)
�3 � 4
5 � 121 � 2
3 � 254 � 5
3 � 10
1 � 2
1 � 5
4.C
LASS
ESA
t Ja
ckso
n H
igh
Sch
ool,
56
of t
he
elev
enth
gra
ders
tak
e ph
ysic
s an
d70
of
them
tak
e bi
olog
y.T
her
e ar
e 40
0el
even
th g
rade
rs i
n t
otal
at
the
sch
ool.
An
ele
ven
th g
rade
r is
ch
osen
at
ran
dom
from
am
ong
all
the
elev
enth
gra
ders
at
the
hig
h s
choo
l.T
he
prob
abil
ity
that
th
e se
lect
ed s
tude
nt
take
s ph
ysic
s an
d
biol
ogy
is
.How
man
y st
ude
nts
at
the
hig
h s
choo
l ta
ke p
hys
ics
or b
iolo
gy?
16
PASS
ENG
ERS
For
Exe
rcis
es 5
an
d 6
,use
the
foll
owin
g in
form
atio
n.
On
an
air
plan
e fl
igh
t,so
me
pass
enge
rstr
avel
wit
h c
arry
-on
lu
ggag
e w
hil
e ot
her
s tr
avel
wit
h a
su
itca
se.S
ome
pass
enge
rs t
rave
l w
ith
car
ry-o
n l
ugg
age
and
a su
itca
se.E
very
one
trav
els
wit
h s
ome
form
of
lugg
age.
5.O
n o
ne
flig
ht,
ther
e w
as n
o pa
ssen
ger
wit
h b
oth
car
ry-o
n l
ugg
age
and
asu
itca
se.O
n t
his
fli
ght
are
the
even
ts
of p
icki
ng
a pa
ssen
ger
wit
h c
arry
-on
lugg
age
and
pick
ing
a pa
ssen
ger
wit
h
a su
itca
se m
utu
ally
exc
lusi
ve?
Yes
6.O
n a
not
her
fli
ght,
ther
e ar
e 12
0pa
ssen
gers
.Of
thos
e 12
0 pa
ssen
gers
,80
hav
e ca
rry-
on l
ugg
age
and
70 h
ave
a su
itca
se.W
hat
is
the
prob
abil
ity
that
a
pass
enge
r h
as b
oth
car
ry-o
n l
ugg
age
and
a su
itca
se?
1 � 4
11 � 40
Cha
pter
12
38G
lenc
oe A
lgeb
ra 2
12-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Prac
tice
Ad
din
g P
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
An
urn
con
tain
s 7
wh
ite
mar
ble
s an
d 5
blu
e m
arb
les.
Fou
r m
arb
les
are
sele
cted
wit
hou
t re
pla
cem
ent.
Fin
d e
ach
pro
bab
ilit
y.
1.P
(4 w
hit
e or
4 b
lue)
� 98 9�2.
P(e
xact
ly 3
wh
ite)
�3 95 9�3.
P(a
t le
ast
3 w
hit
e)�1 34 3�
4.P
(few
er t
han
3 w
hit
e)�1 39 3�
5.P
(3 w
hit
e or
3 b
lue)
�4 99 9�6.
P(n
o w
hit
e or
no
blu
e)� 98 9�
Jas
on a
nd
Mar
ia a
re p
layi
ng
a b
oard
gam
e in
wh
ich
th
ree
dic
e ar
e to
ssed
to
det
erm
ine
a p
laye
r’s
mov
e.F
ind
eac
h p
rob
abil
ity.
7.P
(tw
o 5s
)� 75 2�
8.P
(th
ree
5s)
� 21 16�9.
P(a
t le
ast
two
5s)
� 22 7�
10.P
(no
5s)
�1 22 15 6�11
.P(o
ne
5)�2 75 2�
12.P
(on
e 5
or t
wo
5s)
� 15 2�
Det
erm
ine
wh
eth
er t
he
even
ts a
re m
utu
all
y ex
clu
sive
or i
ncl
usi
ve.T
hen
fin
d t
he
pro
bab
ilit
y.
13.A
cle
rk c
hoos
es 4
CD
pla
yers
at
rand
om fo
r fl
oor
disp
lays
from
a s
hipm
ent
of 2
4 C
D p
laye
rs.
If 1
5 of
the
pla
yers
hav
e a
blue
cas
e an
d th
e re
st h
ave
a re
d ca
se,w
hat
is t
he p
roba
bili
ty o
fch
oosi
ng 4
pla
yers
wit
h a
blue
cas
e or
4 p
laye
rs w
ith
a re
d ca
se?
mu
tual
.exc
lus.
;�57 01 6�
14.A
dep
artm
ent
stor
e em
ploy
s 28
hig
h s
choo
l st
ude
nts
,all
jun
iors
an
d se
nio
rs.S
ix o
f th
e12
sen
iors
are
fem
ales
an
d 12
of
the
jun
iors
are
mal
es.O
ne
stu
den
t em
ploy
ee i
s ch
osen
at r
ando
m.W
hat
is
the
prob
abil
ity
of s
elec
tin
g a
sen
ior
or a
fem
ale?
incl
usi
ve;
�4 7�
15.A
res
tau
ran
t h
as 5
pie
ces
of a
pple
pie
,4 p
iece
s of
ch
ocol
ate
crea
m p
ie,a
nd
3 pi
eces
of
blu
eber
ry p
ie.I
f Ja
nin
e se
lect
s a
piec
e of
pie
at
ran
dom
for
des
sert
,wh
at i
s th
epr
obab
ilit
y th
at s
he
sele
cts
eith
er a
pple
or
choc
olat
e cr
eam
?m
utu
ally
exc
lusi
ve;
�3 4�
16.A
t a
stat
ewid
e m
eeti
ng,t
here
are
20
scho
ol s
uper
inte
nden
ts,1
3 pr
inci
pals
,and
6 a
ssis
tant
prin
cipa
ls.I
f on
e of
th
ese
peop
le i
s ch
osen
at
ran
dom
,wh
at i
s th
e pr
obab
ilit
y th
at h
e or
she
is e
ith
er a
pri
nci
pal
or a
n a
ssis
tan
t pr
inci
pal?
mu
tual
ly e
xclu
sive
;�1 39 9�
17.A
n ai
rlin
e ha
s on
e ba
nk o
f 13
tel
epho
nes
at a
res
erva
tion
s of
fice
.Of
the
13 o
pera
tors
who
wor
k th
ere,
8 ta
ke r
eser
vati
ons
for
dom
esti
c fl
ight
s an
d 5
take
res
erva
tion
s fo
r in
tern
atio
nal
flig
hts
.Sev
en o
f th
e op
erat
ors
taki
ng
dom
esti
c re
serv
atio
ns
and
3 of
th
e op
erat
ors
taki
ng
inte
rnat
ion
al r
eser
vati
ons
are
fem
ale.
If a
n o
pera
tor
is c
hos
en a
t ra
ndo
m,w
hat
is
the
prob
abil
ity
that
th
e pe
rson
ch
osen
tak
es d
omes
tic
rese
rvat
ion
s or
is
a m
ale?
incl
usi
ve;
�1 10 3�
18.M
USI
CF
orty
sen
ior
citi
zen
s w
ere
surv
eyed
abo
ut
thei
r m
usi
c pr
efer
ence
s.T
he
resu
lts
are
disp
laye
d in
th
e V
enn
diag
ram
.If
a se
nio
r ci
tize
n f
rom
th
e su
rvey
gro
up
isse
lect
ed a
t ra
ndo
m,w
hat
is
the
prob
abil
ity
that
he
or
she
like
s on
ly c
oun
try
and
wes
tern
mu
sic?
Wh
at i
s th
epr
obab
ilit
y th
at h
e or
sh
e li
kes
clas
sica
l an
d/or
cou
ntr
y,bu
t n
ot 1
940’
s po
p?� 23 0�
;�2 5�
Co
un
try
and
Wes
tern
1940
’s P
op
Cla
ssic
al
6
9
37 6
54
Chapter 12 A19 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 12-5)
Cha
pter
12
41G
lenc
oe A
lgeb
ra 2
Lesson 12-5
12-5
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Gra
phin
g Ca
lcul
ator
Act
ivit
yP
rob
abili
ties
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
A g
raph
ing
calc
ula
tor
can
be
use
d to
per
form
cal
cula
tion
s in
volv
ing
perm
u-
tati
ons,
com
bin
atio
ns,
and
prob
abil
ity.
Th
ere
are
5 gi
rls
and
3 b
oys
on a
cla
ss c
omm
itte
e.A
su
bco
mm
itte
e of
3 p
eop
le i
s b
ein
g ch
osen
at
ran
dom
.W
hat
is
the
pro
bab
ilit
y th
at t
he
sub
com
mit
tee
wil
l h
ave
at l
east
2 g
irls
?
P(a
t le
ast
2 gi
rls)
�P
(2 g
irls
)�P
(3 g
irls
).E
ach
pro
babi
lity
is
the
prod
uct
of
the
com
bin
atio
ns
of g
irls
an
d bo
ys d
ivid
ed b
y th
e co
mbi
nat
ion
s of
all
th
e st
ude
nts
tak
en 3
at
a ti
me.
Key
stro
kes:
5 3
2 3
3 1
5
3 3
3 3
0 8
3 3
.
Th
e pr
obab
ilit
y th
at t
he
subc
omm
itte
e h
as a
t le
ast
2 gi
rls
is �5 7�.
EN
TER
EN
TER
MA
TH
MA
TH
)
MA
TH
�
MA
TH
+M
AT
H�
MA
TH
(
Fin
d e
ach
pro
bab
ilit
y.
1.T
her
e ar
e 5
girl
s an
d 4
boys
on
th
e sc
hoo
l pu
blic
atio
ns
com
mit
tee.
A g
rou
p of
5 m
embe
rsis
bei
ng c
hose
n at
ran
dom
to
atte
nd a
wor
ksho
p on
sch
ool n
ewsp
aper
s.F
ind
each
pro
babi
lity.
a.at
leas
t 3
girl
sb
.4 g
irls
or
4 bo
ysc.
at le
ast
2 bo
ys
�1 20 1�� 12 25 6�
�1 20 1�
2.T
wo
card
s ar
e dr
awn
fro
m a
sta
nda
rd d
eck
of c
ards
.Fin
d ea
ch p
roba
bili
ty.
a.bo
th q
uee
ns
or b
oth
bla
ckb
.bot
h k
ings
or
both
ace
sc.
both
fac
e ca
rds
or b
oth
bla
ck
� 25 25 1�� 22 21�
�1 68 68 3�
3.F
ind
the
prob
abil
ity
that
a c
omm
itte
e of
6 U
.S.R
epre
sen
tati
ves
sele
cted
at
ran
dom
fro
m
7 D
emoc
rats
an
d 7
Rep
ubl
ican
s w
ill
hav
e at
lea
st 3
Rep
ubl
ican
s on
th
e co
mm
itte
e.�3 40 02 9�
4.T
hre
e C
Ds
are
ran
dom
ly s
elec
ted
from
a c
olle
ctio
n o
f 6
rock
an
d 5
rap
CD
s.F
ind
the
prob
abil
ity
that
at
leas
t 2
are
rock
.�1 39 3�
Tw
o ca
rds
are
ran
dom
ly s
elec
ted
fro
m a
sta
nd
ard
d
eck
of
card
s.F
ind
th
e p
rob
abil
ity
that
bot
h c
ard
sar
e k
ings
or
that
bot
h c
ard
s ar
e re
d.
Sin
ce t
hes
e ev
ents
are
mu
tual
ly i
ncl
usi
ve f
ind
the
com
bin
atio
ns
of 4
kin
gs t
aken
2 a
t a
tim
e pl
us
26 r
ed c
ards
tak
en 2
at
a ti
me
min
us
2re
d ki
ngs
tak
en 2
at
a ti
me
divi
ded
by t
he
com
bin
atio
ns
of 5
2 ca
rds
take
n 2
at
a ti
me.
Key
stro
kes:
4 3
2 26
3
2 2
3 2
52
3 2
.
Th
e pr
obab
ilit
y of
ch
oosi
ng
2 ki
ngs
or
two
red
card
s is
� 25 25 1�.
EN
TER
EN
TER
MA
TH
MA
TH
)
MA
TH
—M
AT
H+
MA
TH
(
Exam
ple
1
Exam
ple
2
Exer
cise
s
Cha
pter
12
40G
lenc
oe A
lgeb
ra 2
12-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
Pro
bab
ility
an
d T
ic-T
ac-T
oe
Wh
at w
ould
be
the
chan
ces
of w
inn
ing
at t
ic-t
ac-t
oe i
f it
wer
e tu
rned
in
to a
gam
e of
pu
re c
han
ce?
To
fin
d ou
t,th
e n
ine
cell
s of
th
e ti
c-ta
c-to
e bo
ard
are
nu
mbe
red
from
1 t
o 9
and
nin
e ch
ips
(als
o n
um
bere
d fr
om 1
to
9) a
re p
ut
into
a b
ag.P
laye
r A
dra
ws
a ch
ip a
t ra
ndo
m a
nd
ente
rs a
n X
in t
he
corr
espo
ndi
ng
cell
.Pla
yer
B d
oes
the
sam
e an
d en
ters
an
O.
To
solv
e th
e pr
oble
m,a
ssu
me
that
bot
h p
laye
rs d
raw
all
th
eir
chip
s w
ith
out
look
ing
and
all
Xan
d O
entr
ies
are
mad
e at
th
e sa
me
tim
e.T
her
e ar
e fo
ur
poss
ible
ou
tcom
es:a
dra
w,A
win
s,B
win
s,an
d ei
ther
A o
r B
can
win
.
Th
ere
are
16 a
rran
gem
ents
th
at r
esu
lt i
n a
dra
w.R
efle
ctio
ns
and
rota
tion
sm
ust
be
cou
nte
d as
sh
own
bel
ow.
o x
ox
o x
o o
xx
o x
4o
o x
4x
x o
8x
o x
x x
oo
x x
Th
ere
are
36 a
rran
gem
ents
in
wh
ich
eit
her
pla
yer
may
win
bec
ause
bot
hpl
ayer
s h
ave
win
nin
g tr
iple
s.
x x
xx
x x
x o
xx
x x
x x
xx
x o
o o
o4
x o
x4
x x
x4
x x
o8
o o
o8
x x
x8
x o
xo
o o
o o
oo
o o
x x
oo
o o
In t
hes
e 36
cas
es,A
’s c
han
ces
of w
inn
ing
are
�1 43 0�.
1.F
ind
the
12 a
rran
gem
ents
in
wh
ich
B w
ins
and
A c
ann
ot.
o o
xo
x o
x o
x8
x o
x4
x x
ox
x o
2.B
elow
are
12
of t
he
arra
nge
men
ts i
n w
hic
h A
win
s an
d B
can
not
.Wri
teth
e n
um
bers
to
show
th
e re
flec
tion
s an
d ro
tati
ons
for
each
arr
ange
men
t.W
hat
is
the
tota
l n
um
ber?
62
o x
ox
o x
x x
xx
x x
x o
ox
o o
x x
x1
o x
o1
x o
o4
o x
o4
x x
x4
x x
o4
o x
ox
o x
x o
oo
x o
o o
xo
o x
x x
ox
x x
x x
xx
x x
x o
ox
x o
o x
x4
o x
o8
x o
o8
x o
o8
x x
x8
o x
o8
o o
xo
o x
o x
oo
o x
o x
ox
o x
3.T
her
e ar
e � (5
9 !4! !)�
diff
eren
t an
d eq
ual
ly p
roba
ble
dist
ribu
tion
s.C
ompl
ete
the
char
t to
fin
d th
e pr
obab
ilit
y fo
r a
draw
or
for
A o
r B
to
win
.
Dra
w:
�
Aw
ins:
�
�1 43 0��
��
B w
ins:
�
�12
142
027
36
40( 126
)12 12
6
737
1260
36 � 126
62 126
8 6316 � 12
6
Chapter 12 A20 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 12-6)
Cha
pter
12
43G
lenc
oe A
lgeb
ra 2
Lesson 12-6
12-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Sta
tist
ical
Mea
sure
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Mea
sure
s o
f C
entr
al T
end
ency
Use
Wh
en
Mea
sure
s o
fm
ean
the
data
are
spr
ead
out
and
you
wan
t an
ave
rage
of
valu
es
Cen
tral
Ten
den
cym
edia
nth
e da
ta c
onta
in o
utlie
rs
mod
eth
e da
ta a
re t
ight
ly c
lust
ered
aro
und
one
or t
wo
valu
es
Fin
d t
he
mea
n,m
edia
n,a
nd
mod
e of
th
e fo
llow
ing
set
of d
ata:
{42,
39,3
5,40
,38,
35,4
5}.
To
fin
d th
e m
ean
,add
th
e va
lues
an
d di
vide
by
the
nu
mbe
r of
val
ues
.
mea
n �
�39
.14.
To
fin
d th
e m
edia
n,a
rran
ge t
he
valu
es i
n a
scen
din
g or
des
cen
din
g or
der
and
choo
se t
he
mid
dle
valu
e.(I
f th
ere
is a
n e
ven
nu
mbe
r of
val
ues
,fin
d th
e m
ean
of
the
two
mid
dle
valu
es.)
In t
his
cas
e,th
e m
edia
n i
s 39
.T
o fi
nd
the
mod
e,ta
ke t
he
mos
t co
mm
on v
alu
e.In
th
is c
ase,
the
mod
e is
35.
Fin
d t
he
mea
n,m
edia
n,a
nd
mod
e of
eac
h s
et o
f d
ata.
Rou
nd
to
the
nea
rest
hu
nd
red
th,i
f n
eces
sary
.
1.{2
38,2
61,2
45,2
49,2
55,2
62,2
41,2
45}
249.
5;24
7;24
5
2.{9
,13,
8,10
,11,
9,12
,16,
10,9
}10
.7;
10;
9
3.{1
20,1
08,1
45,1
29,1
02,1
32,1
34,1
18,1
08,1
42}
123.
8;12
4.5;
108
4.{6
8,54
,73,
58,6
3,72
,65,
70,6
1}64
.89;
65;
no
mo
de
5.{3
4,49
,42,
38,4
0,45
,34,
28,4
3,30
}38
.3;
39;
34
6.T
he
tabl
e at
th
e ri
ght
show
s th
e po
pula
tion
s of
th
e
six
New
En
glan
d ca
pita
ls.W
hic
h w
ould
be
the
mos
t ap
prop
riat
e m
easu
re o
f ce
ntr
al t
ende
ncy
to
repr
esen
t th
e da
ta?
Exp
lain
wh
y an
d fi
nd
that
val
ue.
Th
ere
is n
o m
od
e.T
he
po
pu
lati
on
of
Bo
sto
n
is a
n o
utl
ier
and
wo
uld
rai
se t
he
mea
n
too
hig
h.T
he
med
ian
,79,
500,
wo
uld
be
the
bes
t ch
oic
e.
42 �
39 �
35 �
40 �
38 �
35 �
45�
��
��
7
Exam
ple
Exer
cise
s
Sour
ce: w
ww.fa
ctfin
der.c
ensu
s.gov
Cit
yP
op
ula
tio
n (
rou
nd
edto
th
e n
eare
st 1
000)
Aug
usta
, M
E19
,000
Bos
ton,
MA
589,
000
Con
cord
, N
H37
,000
Har
tford
, C
T12
2,00
0
Mon
tpel
ier,
VT
8,00
0
Pro
vide
nce,
RI
174,
000
Cha
pter
12
42G
lenc
oe A
lgeb
ra 2
12-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Sta
tist
ical
Mea
sure
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
2-6
in y
our
text
boo
k.
Th
ere
is m
ore
than
on
e w
ay t
o gi
ve a
n “
aver
age”
scor
e fo
r th
is t
est.
Th
ree
mea
sure
s of
cent
ral
tend
ency
for
the
se s
core
s ar
e 94
,76.
5 an
d 73
.9.C
an y
ou t
ell
whi
ch o
f th
ese
is t
hem
ean,
the
med
ian,
and
the
mod
e w
itho
ut d
oing
any
cal
cula
tion
s? E
xpla
in y
our
answ
er.
Sam
ple
an
swer
:Yes
.Th
e m
od
e m
ust
be
on
e o
f th
e sc
ore
s,so
it m
ust
be
anin
teg
er.T
he
med
ian
mu
st b
e ei
ther
on
e o
f th
e sc
ore
s o
r h
alfw
ay b
etw
een
two
of
the
sco
res,
so it
mu
st b
e an
inte
ger
or
a d
ecim
al e
nd
ing
wit
h .5
.T
her
efo
re,9
4 is
th
e m
od
e,76
.5 is
th
e m
edia
n,a
nd
73.
9 is
th
e m
ean
.
Rea
d t
he
Less
on
1.M
atch
eac
h m
easu
re w
ith
on
e of
th
e si
x de
scri
ptio
ns
of h
ow t
o fi
nd
mea
sure
s of
cen
tral
ten
den
cy a
nd
vari
atio
n.
a.m
edia
nvi
b.m
ode
ic.
ran
geiv
d.
vari
ance
iiie.
mea
nii
f.st
anda
rd d
evia
tion
v
i.F
ind
the
mos
t co
mm
only
occ
urr
ing
valu
es o
r va
lues
in
a s
et o
f da
ta.
ii.A
dd t
he
data
an
d di
vide
by
the
nu
mbe
r of
ite
ms.
iii.
Fin
d th
e m
ean
of
the
squ
ares
of
the
diff
eren
ces
betw
een
eac
h v
alu
e in
th
e se
t of
dat
aan
d th
e m
ean
.
iv.
Fin
d th
e di
ffer
ence
bet
wee
n t
he
larg
est
and
smal
lest
val
ues
in
th
e se
t of
dat
a.
v.T
ake
the
posi
tive
squ
are
root
of
the
vari
ance
.
vi.I
f th
ere
is a
n o
dd n
um
ber
of i
tem
s in
a s
et o
f da
ta,t
ake
the
mid
dle
one.
If t
her
e is
an
even
nu
mbe
r of
ite
ms,
add
the
two
mid
dle
item
s an
d di
vide
by
2.
Rem
emb
er W
hat
Yo
u L
earn
ed
2.It
is
usu
ally
eas
ier
to r
emem
ber
a co
mpl
icat
ed p
roce
dure
if
you
bre
ak i
t do
wn
in
to s
teps
.W
rite
th
e pr
oced
ure
for
fin
din
g th
e st
anda
rd d
evia
tion
for
a s
et o
f da
ta i
n a
ser
ies
ofbr
ief,
nu
mbe
red
step
s.
Sam
ple
an
swer
:1.
Fin
d t
he
mea
n.
2.F
ind
th
e d
iffe
ren
ce b
etw
een
eac
h v
alu
e an
d t
he
mea
n.
3.S
qu
are
each
dif
fere
nce
.4.
Fin
d t
he
mea
n o
f th
e sq
uar
es.
5.Ta
ke t
he
po
siti
ve s
qu
are
roo
t.
Chapter 12 A21 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lesson 12-6)
Cha
pter
12
45G
lenc
oe A
lgeb
ra 2
Lesson 12-6
12-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceS
tati
stic
al M
easu
res
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Fin
d t
he
vari
ance
an
d s
tan
dar
d d
evia
tion
of
each
set
of
dat
a to
th
e n
eare
st t
enth
.
1.{3
2,41
,35,
35,4
6,42
}23
.6,4
.9
2.{1
3,62
,77,
24,3
8,19
,88}
763.
8,27
.6
3.{8
9,99
,42,
16,4
2,71
,16}
959.
1,31
.0
4.{4
50,4
00,6
25,2
25,3
00,7
50,6
50,6
25}
30,5
37.1
;17
4.7
5.{1
7,23
,65,
94,3
3,33
,33,
8,57
,75,
44,1
2,11
,68,
39}
630.
7,25
.1
6.{7
.2,3
.1,3
.8,9
.5,8
.3,8
.4}
5.8,
2.4
7.{1
.5,2
.5,3
.5,4
.5,4
.5,5
.5,6
.5,7
.5}
3.5,
1.9
For
Exe
rcis
es 8
an
d 9
,use
th
e ta
ble
th
at s
how
s th
e p
rofi
t in
bil
lion
s of
dol
lars
rep
orte
d b
y U
.S.m
anu
fact
ure
rs f
or t
he
firs
t q
uar
ter
of t
he
year
s fr
om 1
997
thro
ugh
200
1.
Sour
ce: U
. S. C
ensu
s Bur
eau
8.F
ind
the
mea
n an
d m
edia
n of
the
dat
a to
the
nea
rest
ten
th.
$64.
3 b
illio
n,$
61.4
bill
ion
9.W
hic
h m
easu
re o
f ce
ntr
al t
ende
ncy
bes
t re
pres
ents
th
e da
ta?
Exp
lain
.T
he
med
ian
is m
ore
rep
rese
nta
tive
bec
ause
th
e va
lue
45.3
is n
ot
clo
se t
oth
e o
ther
dat
a p
oin
ts,a
nd
it lo
wer
s th
e m
ean
.
For
Exe
rcis
es 1
0 an
d 1
1,u
se t
he
tab
le t
hat
sh
ows
the
per
cen
t of
fou
rth
gra
de
stu
den
ts r
ead
ing
at o
r ab
ove
the
pro
fici
ency
lev
el i
n a
nat
ion
ally
-ad
min
iste
red
read
ing
asse
ssm
ent.
Sour
ce: N
atio
nal C
ente
r for
Edu
catio
n St
atist
ics
10.F
ind
the
mea
n,m
edia
n,a
nd
stan
dard
dev
iati
on o
f th
e da
ta t
o th
e n
eare
st t
enth
.30
.5%
,30.
5%,1
.1%
11.W
hat
do
the
stat
isti
cs f
rom
Exe
rcis
e 11
tel
l yo
u a
bou
t th
e da
ta?
Sam
ple
an
swer
:S
ince
th
e m
edia
n a
nd
mea
n a
re e
qu
al a
nd
th
e st
and
ard
dev
iati
on
is s
mal
l,th
e p
erce
nt
of
stu
den
ts r
ead
ing
at
or
abov
e th
ep
rofi
cien
cy le
vel h
as n
ot
vari
ed m
uch
fro
m 1
992
to 2
000.
Year
1992
1994
1998
2000
Per
cen
t at
or
abov
e p
rofi
cien
cy le
vel
29%
30%
31%
32%
Year
1997
1998
1999
2000
2001
Sea
son
ally
-Ad
just
ed
Pro
fit
($ b
illio
ns)
$61.
4$7
5.6
$60.
9$7
8.5
$45.
3
Cha
pter
12
44G
lenc
oe A
lgeb
ra 2
12-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(co
nti
nued
)
Sta
tist
ical
Mea
sure
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
Mea
sure
s o
f V
aria
tio
nT
he
ran
gean
d th
e st
and
ard
dev
iati
onm
easu
re h
owsc
atte
red
a se
t of
dat
a is
.
Sta
nd
ard
If a
set
of d
ata
cons
ists
of
the
nva
lues
x1,
x2,
…,
x nan
d ha
s m
ean
x �, t
hen
the
stan
dard
dev
iatio
n
Dev
iati
on
is g
iven
by
��
���
.
Th
e sq
uar
e of
th
e st
anda
rd d
evia
tion
is
call
ed t
he
vari
ance
.
Fin
d t
he
vari
ance
an
d s
tan
dar
d d
evia
tion
of
the
dat
a se
t {1
0,9,
6,9,
18,4
,8,2
0}.
Ste
p 1
Fin
d th
e m
ean
.
x ��
�10
.5
Ste
p 2
Fin
d th
e va
rian
ce.
�2
�S
tand
ard
varia
nce
form
ula
� �or
27.
5
Ste
p 3
Fin
d th
e st
anda
rd d
evia
tion
.�
��
27.5
��
5.2
Th
e va
rian
ce i
s 27
.5 a
nd
the
stan
dard
dev
iati
on i
s ab
out
5.2.
Fin
d t
he
vari
ance
an
d s
tan
dar
d d
evia
tion
of
each
set
of
dat
a.R
oun
d t
o th
en
eare
st t
enth
.
1.{1
00,8
9,11
2,10
4,96
,108
,93}
2.{6
2,54
,49,
62,4
8,53
,50}
58.5
;7.
629
.4;
5.4
3.{8
,9,8
,8,9
,7,8
,9,6
}4.
{4.2
,5.0
,4.7
,4.5
,5.2
,4.8
,4.6
,5.1
}0.
9;0.
90.
1;0.
3
5.T
he
tabl
e at
th
e ri
ght
list
s th
e pr
ices
of
ten
bra
nds
of
brea
kfas
t ce
real
.Wh
at i
s th
e st
anda
rd d
evia
tion
of
the
valu
es t
o th
e n
eare
st p
enn
y?$0
.33
Pri
ce o
f 10
Bra
nd
so
f B
reak
fast
Cer
eal
$2.2
9$3
.19
$3.3
9$2
.79
$2.9
9$3
.09
$3.1
9$2
.59
$2.7
9$3
.29
220
�8(10
�10
.5)2
�(9
�10
.5)2
�…
�(2
0 �
10.5
)2�
��
��
�8
(x1
�x �)
2�
(x2
�x �)
2�
… �
(xn
�x �)
2�
��
��
n
10 �
9 �
6 �
9 �
18 �
4 �
8 �
20�
��
��
8
(x1
�x �)
2�
(x2
�x �)
2�
… �
(xn
�x �)
2
��
��
�n
Exam
ple
Exer
cise
s
Chapter 12 A22 Glencoe Algebra 2
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Answers (Lesson 12-6)
Cha
pter
12
47G
lenc
oe A
lgeb
ra 2
Lesson 12-6
12-6
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Sta
tist
ical
Mea
sure
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1.SP
OR
TST
he
tabl
e be
low
sh
ows
the
nu
mbe
r of
tim
es s
ome
team
s in
th
eN
atio
nal
Foo
tbal
l L
eagu
e h
ave
won
th
e S
upe
r B
owl.
Sour
ce:w
ww.p
ubqu
izhelp
.34s
p.co
m
Wh
ich
sta
tist
ical
mea
sure
rep
rese
nts
the
team
(s)
wit
h t
he
leas
t S
upe
r B
owl
vict
orie
s?th
e m
od
e
2.SA
LAR
IES
Th
e m
edia
n s
alar
y in
a
smal
l co
mpa
ny
is $
10.2
0 pe
r h
our.
Wh
at p
erce
nta
ge o
f th
e em
ploy
ees
at
the
com
pan
y ea
rns
mor
e th
an $
10.2
0pe
r h
our?
50%
3.R
AN
DO
M G
ENER
ATO
RS
Sam
uel
has
wri
tten
a c
ompu
ter
prog
ram
to
gen
erat
ea
ran
dom
sel
ecti
on o
f th
e fo
llow
ing
two-
digi
t n
um
bers
.
25,6
7,54
,99,
41,8
7,90
,18,
32
Fin
d th
e m
ean
,med
ian
,an
d m
ode
ofth
is d
ata.
57;
54;
no
ne
Nu
mb
er o
fN
FL
Tea
mS
up
er B
ow
lV
icto
ries
New
Eng
land
3
Bal
timor
e2
Kan
sas
City
1
St.
Loui
s1
Den
ver
2
Gre
en B
ay1
Dal
las
5
San
Fra
ncis
co5
Oak
land
2
Pitt
sbur
gh5
Mia
mi
2
Was
hing
ton
3
NY
Gia
nts
2
NY
Jet
s1
Chi
cago
1
4.H
EIG
HTS
Th
e fo
llow
ing
tabl
e li
sts
the
hei
ghts
of
som
e of
th
e gr
eat
NB
Apl
ayer
s.
Sour
ce:w
ww.si
dwell
.edu
Fin
d th
e m
ean
an
d st
anda
rd d
evia
tion
of
th
e da
ta i
n t
he
tabl
e.R
oun
d yo
ur
answ
er t
o th
e n
eare
st h
un
dred
th.
83;
3.0
MET
EOR
SF
or E
xerc
ises
5-8
,use
th
efo
llow
ing
info
rmat
ion
.
Arl
ene
stay
ed u
p la
te o
ne
nig
ht
to w
atch
th
e P
erse
id m
eteo
r sh
ower
.Sh
e re
cord
ed
the
nu
mbe
r of
met
eors
sh
e sa
w e
very
ten
min
ute
s st
arti
ng
at 1
A.M
.an
d go
ing
un
til
4 A
.M.H
er d
ata
are
show
n b
elow
.8,
7,8,
12,1
7,15
,22,
28,2
9,31
,28,
23,2
9,28
,25,
23,1
5,12
5.W
hat
is
the
mea
n o
f th
is d
ata
set?
20
6.W
hat
is
the
med
ian
of
this
dat
a se
t?22
.5
7.W
hat
is
the
mod
e of
th
is d
ata
set?
28
8.W
hat
is
the
stan
dard
dev
iati
on o
f th
isda
ta s
et?
Rou
nd
you
r an
swer
to
the
nea
rest
hu
ndr
edth
.8.
05
Pla
yer
Hei
gh
t(i
n in
ches
)
Kar
eem
Abd
ul-J
abba
r86
Larr
y B
ird81
Sha
quill
e O
’Nea
l85
Wilt
Cha
mbe
rlain
85
Mic
hael
Jor
dan
78
Cha
pter
12
46G
lenc
oe A
lgeb
ra 2
12-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Prac
tice
Sta
tist
ical
Mea
sure
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Fin
d t
he
vari
ance
an
d s
tan
dar
d d
evia
tion
of
each
set
of
dat
a to
th
e n
eare
st t
enth
.
1.{4
7,61
,93,
22,8
2,22
,37}
2.{1
0,10
,54,
39,9
6,91
,91,
18}
673.
1,25
.912
28.6
,35.
1
3.{1
,2,2
,3,3
,3,4
,4,4
,4,5
,5,5
,5,5
}4.
{110
0,72
5,85
0,33
5,70
0,80
0,95
0}1.
6,1.
249
,150
.0;
221.
7
5.{3
.4,7
.1,8
.5,5
.1,4
.7,6
.3,9
.9,8
.4,3
.6}
6.{2
.8,0
.5,1
.9,0
.8,1
.9,1
.5,3
.3,2
.6,0
.7,2
.5}
4.7,
2.2
0.8,
0.9
7.H
EALT
H C
AR
EE
igh
t ph
ysic
ian
s w
ith
15
pati
ents
on
a h
ospi
tal
floo
r se
e th
ese
pati
ents
an a
vera
ge o
f 18
min
ute
s a
day.
Th
e 22
nu
rses
on
th
e sa
me
floo
r se
e th
e pa
tien
ts a
nav
erag
e of
3 h
ours
a d
ay.A
s a
hos
pita
l ad
min
istr
ator
,wou
ld y
ou q
uot
e th
e m
ean
,m
edia
n,o
r m
ode
as a
n i
ndi
cato
r of
th
e am
oun
t of
dai
ly m
edic
al a
tten
tion
th
e pa
tien
ts o
nth
is f
loor
rec
eive
? E
xpla
in.
Eit
her
th
e m
edia
n o
r th
e m
od
e;th
ey a
re e
qu
al a
nd
hig
her
th
an t
he
mea
n,w
hic
h is
low
ered
by
the
smal
ler
amo
un
t o
f ti
me
the
phy
sici
ans
spen
d w
ith
th
e p
atie
nts
.
For
Exe
rcis
es 8
–10,
use
th
e fr
equ
ency
tab
le t
hat
sh
ows
the
per
cen
t of
pu
bli
c sc
hoo
lte
ach
ers
in t
he
U.S
.in
199
9 w
ho
use
d c
omp
ute
rs o
r th
eIn
tern
et a
t sc
hoo
l fo
r va
riou
sad
min
istr
ativ
e an
d t
each
ing
acti
viti
es.
8.F
ind
the
mea
n,m
edia
n,an
d m
ode
of t
he
data
.17
.75%
,12%
,8%
9.S
uppo
se y
ou b
elie
ve t
each
ers
use
com
pute
rs o
r th
e In
tern
et t
ooin
freq
uen
tly.
Wh
ich
mea
sure
w
ould
you
quo
te a
s th
e “a
vera
ge?”
Sour
ce: N
atio
nal A
sses
smen
t of E
duca
tiona
l Pro
gres
s
Exp
lain
.M
od
e;it
is lo
wes
t.
10.S
upp
ose
you
bel
ieve
tea
cher
s u
se c
ompu
ters
or
the
Inte
rnet
too
oft
en.W
hic
h m
easu
rew
ould
you
qu
ote
as t
he
“ave
rage
?”E
xpla
in.
Mea
n;
it is
hig
hes
t.
For
Exe
rcis
es 1
1 an
d 1
2,u
se t
he
freq
uen
cy t
able
th
at
show
s th
e n
um
ber
of
gam
es p
laye
d b
y 24
Am
eric
an
Lea
gue
bas
ebal
l p
laye
rs b
etw
een
op
enin
g d
ay,2
001
and
Sep
tem
ber
8,2
001.
11.F
ind
the
mea
n,m
edia
n,m
ode,
and
stan
dard
dev
iati
on o
f th
en
um
ber
of g
ames
pla
yed
to t
he
nea
rest
ten
th.
138.
2,13
8;13
8,2.
0
12.F
or h
ow m
any
play
ers
is t
he
nu
mbe
r of
gam
es w
ith
in o
ne
stan
dard
dev
iati
on o
f th
e m
ean
?14
No
.of
Gam
esF
req
uen
cy
141
4
140
3
139
4
138
5
137
2
136
3
135
3
Per
cen
t U
sin
g
Act
ivit
yC
om
pu
ter
or
Inte
rnet
Cre
ate
inst
ruct
iona
l mat
eria
ls39
Adm
inis
trat
ive
reco
rd k
eepi
ng34
Com
mun
icat
e w
ith c
olle
ague
s23
Gat
her
info
rmat
ion
for
plan
ning
less
ons
16
Mul
timed
ia c
lass
room
pre
sent
atio
ns8
Acc
ess
rese
arch
and
bes
t pr
actic
es fo
r te
achi
ng8
Com
mun
icat
e w
ith p
aren
ts o
r st
uden
ts8
Acc
ess
mod
el le
sson
pla
ns6
Sour
ce:M
ajor L
eagu
e Ba
seba
ll
Chapter 12 A23 Glencoe Algebra 2
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Answers (Lessons 12-6 and 12-7)
Cha
pter
12
49G
lenc
oe A
lgeb
ra 2
Lesson 12-7
12-7
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Read
ing
to L
earn
Mat
hem
atic
sT
he
No
rmal
Dis
trib
uti
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
2-7
in y
our
text
boo
k.
Th
ere
wer
e 66
pla
yers
on
th
e te
am a
nd
the
mea
n h
eigh
t w
as a
ppro
xim
atel
y 74
.1.A
bou
tw
hat
fra
ctio
n o
f th
e pl
ayer
s’ h
eigh
ts a
re b
etw
een
72
and
75,i
ncl
usi
ve?
Sam
ple
an
swer
:ab
ou
t�1 2�
Rea
d t
he
Less
on
1.In
dica
te w
het
her
eac
h o
f th
e fo
llow
ing
stat
emen
ts i
s tr
ue
or f
alse
.
a.In
a c
onti
nu
ous
prob
abil
ity
dist
ribu
tion
,th
ere
is a
fin
ite
nu
mbe
r of
pos
sibl
e ou
tcom
es.
fals
e
b.
Eve
ry n
orm
al d
istr
ibu
tion
can
be
repr
esen
ted
by a
bel
l cu
rve.
tru
e
c.A
dis
trib
uti
on t
hat
is
repr
esen
ted
by a
cu
rve
that
is
hig
h a
t th
e le
ft a
nd
has
a t
ail
toth
e ri
ght
is n
egat
ivel
y sk
ewed
.fa
lse
d.
A n
orm
al d
istr
ibu
tion
is
an e
xam
ple
of a
ske
wed
dis
trib
uti
on.
fals
e
2.M
s.R
ose
gave
the
sam
e qu
iz t
o he
r tw
o ge
omet
ry c
lass
es.S
he r
ecor
ded
the
follo
win
g sc
ores
.
Fir
st-p
erio
d c
lass
:
Fif
th-p
erio
d c
lass
:
In e
ach
cla
ss,3
0 st
ude
nts
too
k th
e qu
iz.T
he
mea
n s
core
for
eac
h c
lass
was
6.4
.Wh
ich
set
of s
core
s h
as t
he
grea
ter
stan
dard
dev
iati
on?
(An
swer
th
is q
ues
tion
wit
hou
t do
ing
any
calc
ula
tion
s.)
Exp
lain
you
r an
swer
.
Fir
st p
erio
d c
lass
;sa
mp
le a
nsw
er:T
he
sco
res
are
mo
re s
pre
ad o
ut
fro
mth
e m
ean
th
an f
or
the
fift
h p
erio
d c
lass
.
Rem
emb
er W
hat
Yo
u L
earn
ed
3.M
any
stu
den
ts h
ave
trou
ble
rem
embe
rin
g h
ow t
o de
term
ine
if a
cu
rve
repr
esen
ts a
dist
ribu
tion
th
at i
s po
siti
vely
ske
wed
or n
egat
ivel
y sk
ewed
.Wh
at i
s an
eas
y w
ay t
ore
mem
ber
this
?
Sam
ple
an
swer
:F
ollo
w t
he
tail!
If t
he
tail
is o
n t
he
rig
ht
(po
siti
ved
irec
tio
n),
the
dis
trib
uti
on
is p
osi
tive
ly s
kew
ed.I
f th
e ta
il is
on
th
e le
ft(n
egat
ive
dir
ecti
on
),th
e d
istr
ibu
tio
n is
neg
ativ
ely
skew
ed.
Sco
re0
12
34
56
78
910
Fre
qu
ency
00
00
34
97
61
0
Sco
re0
12
34
56
78
910
Fre
qu
ency
10
10
34
57
43
2
Cha
pter
12
48G
lenc
oe A
lgeb
ra 2
12-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Enri
chm
ent
Sta
nd
ard
Dev
iati
on
of
Sam
ple
Dat
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
A p
opu
lati
onis
th
e se
t of
all
mea
sure
men
ts o
f in
tere
st t
o an
in
vest
igat
or.
A s
ampl
eis
a s
ubs
et o
f m
easu
rem
ents
sel
ecte
d fr
om t
he
popu
lati
on
of i
nte
rest
.A s
tati
stic
is a
ny
quan
tity
wh
ose
valu
e ca
n b
e ca
lcu
late
d fr
omsa
mpl
e da
ta.A
com
mon
mis
take
is
to u
se t
he
term
s pr
obab
ilit
yan
d st
atis
tics
inte
rch
ange
ably
.Pro
babi
liti
es a
re u
sed
to m
ake
stat
emen
ts f
rom
a
popu
lati
on t
o a
sam
ple,
but
stat
isti
cs a
re c
alcu
late
d fr
om a
sam
ple
and
are
to m
ake
infe
ren
ces
abou
t a
popu
lati
on.
Th
e ra
nge
is a
sta
tist
ic c
alcu
late
d by
tak
ing
the
diff
eren
ce b
etw
een
th
e la
rges
t ob
serv
atio
n a
nd
the
smal
lest
obs
erva
tion
.Ran
ge �
x max
�x m
in.
Th
e sa
mpl
e va
rian
ceis
cal
cula
ted
usi
ng
the
form
ula
:s2
�w
her
e x �
is t
he
sam
ple
mea
n.T
her
efor
e,th
e sa
mpl
e st
and
ard
dev
iati
onis
th
e sq
uar
e
root
of
the
sam
ple
vari
ance
,s�
�s2 �
.
To
calc
ula
te t
he
sam
ple
vari
ance
:
1.C
alcu
late
th
e sa
mpl
e m
ean
.For
exa
mpl
e,su
ppos
e a
sam
ple
con
tain
s th
e
nu
mbe
rs {
2,5,
6,9,
11}.
Th
e sa
mpl
e m
ean
is
x ��
�6.
6.
2.N
ext
use
th
e fo
rmu
la a
bove
to
calc
ula
te t
he
sam
ple
vari
ance
,in
th
is c
ase:
s2�
�12
.3.
3.F
inal
ly,t
he
sam
ple
stan
dard
dev
iati
on i
s eq
ual
to
3.50
7 by
tak
ing
the
squ
are
root
of
12.3
.
1.W
hat
are
som
e di
ffer
ence
s in
th
e fo
rmu
la f
or t
he
sam
ple
vari
ance
com
pare
d to
th
e fo
rmu
la f
or t
he
popu
lati
on v
aria
nce
?It
use
s th
e sa
mp
le m
ean
inst
ead
of
the
po
pu
lati
on
mea
n,a
nd
sin
ce t
he
sam
ple
mea
n is
an
est
imat
or
for
the
po
pu
lati
on
mea
n,t
he
den
om
inat
or
is n
�1
inst
ead
of
n.
2.G
iven
th
e ra
ndo
m s
ampl
e {5
,7,1
,2,4
},fi
nd
the
sam
ple
vari
ance
.5.
70
3.C
alcu
late
th
e sa
mpl
e st
anda
rd d
evia
tion
.2.
387
4.C
alcu
late
th
e ra
nge
of
the
sam
ple
data
{5,
7,1,
2,4}
.6
5.A
n a
ppro
xim
atio
n f
or t
he
sam
ple
stan
dard
dev
iati
on i
s gi
ven
by:
s�
.C
ompa
re t
his
an
swer
to
you
r an
swer
fro
m 3
.6
Ran
ge�
4
(6.6
�2)
2�
(6.6
�5)
2�
(6.6
�6)
2�
(6.6
�9)
2�
(6.6
�11
)2�
��
��
��
�4
2 �
5 �
6 �
9 �
11�
��
5
n
i�1
(x ��
x i)2
��
n�
1
Exer
cise
s
