Name: r-N Date:

MDM 4U UNIT 6 (CHAPTER 7 TEST)

PROBABILITY

K&U APP COM TIPS

20 20 14 Level 4

Key Equations: Discrete Uniform Distribution:

Binomial Distribution:

Geometric Distribution:

Hypergeometric Distribution:

P(X) =

P(x) = (:) px qn -x

P(x) = qxp

(a)(n-a) P (X) = xik77,—

) x)

E(X) = Eri`.1 xiP(xi)

E(X) = np

E(X) =

E(X) = ra

1. Determine the type of probability distribution you would use for the following: (4K) a. Rolling a dice and counting the number of sixes you roll on 10 tries.

lej orr''

b. Drawing cards from a deck without replacing them and counting how many diamonds you get.

4kg e_Vat_OINAQ)rn:

c. Finding out the probability of flipping heads exactly 5 times before you flip tails.

e eomQ...-+rk • c d. Finding the probability of rolling a 7 on a 12 sided dice.

sce.e_etc u c-or tyl (10L.K1- ks)

2. Nicole designed a board game that uses a spinner with 3 equal sectors numbered 1, 2, 3; and a

standard six sided die. The player will spin the spinner and roll the die and move his/her pawn the

number of spaces equal to the sum of the spinner and die.

a. Create a grid showing all of the possible outcomes. (1K)

\ 2- 6 "i 5 L.

2. 3 'A 5 7

3 5 (0 7

G 1 9 1

X P(X=:..)

LI iZ

3/la -7 --2-h

9 2/8

'AZ

e.

/`

2 m

tl k4

I, ill

t1 What is the expected value of this Rando VariabTe? K, 11

Name:

Date:

b. Create a probability distribution table and graph for the Random Variable that is defined to be

the number of squares a player moves after spinning the spinner and rolling the die. (4K)

2(fe), 3(e)+ 44(18) .t- ((Mg) -1- 1( 3/Ice 240 +9( 14)

2 + 12- +. -T

A._ gd

t ea

11

% 2 7 5.5

c. Is it a "fair" spinner? What would happen if the spinner is "fair"? (2K)

No --E-V\Q_ 5F\ ; s ncyk biz_ca,Kst e(?c)

I (0 9 I CR'

3. Rachel is a soccer player for the

Highland Hawks. During the

season she was successful of 15

of 20 penalty kicks. If she was to

take three penalty kicks in

practice, you could use her past

success rate to estimate the

probability of the number of

times she will score out of her

three attempts.

a. Create a probability

distribution for the

Random Variable

defined to be the

number of times she

scores on her three

x P(X=x)

P(c) = ( )( 1) Q (10) 3 __ 6'4 ' 1 ' S-4" 70

P CI) "C) ( tiY ( +1) 1

1- 30 -- 1 q , Ofo %,

-P( 2-) ' (1-)(1) 2-(+4) 1 Z-

lilLk ' 4-1,'2 ∎ 191

3 PCS) ' (3 )( ) 3(i) *

z-- a] - 47. \ct 74., t--;-,k - penalty kick attempts in practice. (4K)

2

Name: Date:

b. Show two ways to calculate the probability that she does not score on all three. (4A)

x * P(0) .P( k PC 2-)

3-1 51.

`-t ( s a Si. eiv\o"Ce.

s one will cyk sc_cyc all 4. Assuming that the probability of being born on a particular day of the week is equal for all days,

determine the probability that in a random sample of 10 students that more than 2 students were born on a weekend. (4A, 1C)

"•\ ( \ or 5

)k

v ) ,-A

) )

0 24 - `23 - 0 2ctq

4 0

0 0

_ s S 714 Ck.kv\ce

-k)kr\ok ktAciviN 2 s-I-t~cL.r{s

w-t \Awn 5. A committee of six athletes is to be randomly selected from a group of 10 hockey players and 12

football players. Let X be the random variable defined to be the number football players that were selected to the committee. The random variable X is Hyper-Geometric.

a. What are the values of a, r, and n in this distribution?(2K)

n ,nv,,m1oer ortvx k!--00-000Ak p\441e,,-,

c = sivoe-kAr cy- oer1-riscx.k\ f;.00-aex-s

Y N u-wx1r)vf- a Ote_opte Apo( -f- ifec

= N 04-1 11 Oa-we.rs we_ kA)a-nr‘r- a r\ Comm b. Use the distribution formula to calculate the probability of exactly 3 football players being

selected for the committee. (2A

(o PC_) =- 3 3 C Z2

(2 20) ( 0_0 ')

1 y Co It

-= b ,

41,,, erptoolooittj v\aukrk5 ey,a_c_t-iti 3

plat sow cowl witif-e( s 3S" °)6

3

Name: Date:

c. What is the expected number of football players in the selection? (1A,1C)

ra

S. ZR- or -emit-Ica-11 e

e...)efec t-ecl 4 -0 19

44‘.,2 commt

6. A game consists of rolling a single die. If you roll an even number, you win 10 points. If you roll an odd

number, you lose three times the amount of points shown on the die.

a. What is the expected value of this game?(3A)

AtZt '1) ()C ) X I X ft S ) C-k..?( ) - - 34 4 - t — ° 1% t (n-(sz4 12-, 1 n -3 - 0 -. S 2 Yfe +I b ÷ 1Y6 6 '2_

3 4 - 9 -Vt. 4 lb tic. 4 174.,

5 yb -is- -in

6 14 +to +1 yig,

b. What does the expected value mean in this game? Is it "fair"?(2C)

elo to tomes ertv.imit 5 a vvtout n-f- 04- poi nig

I-PvL -fyr)wi p (cvylvNi avvt_e_ 51VICL

ECK ) o (4- is ifc=v3k---

7. Approximately 5% of the first batch of engines off a new production line have flaws. Six engines are

randomly selected from the production line, and tested for flaws.

a. What is the probability that exactly 2 will be flawed engines? (2A,1C)

?Lx) = 4).5-) s-)" i ts) -40) Lo ? I t's--)

solos-

a\sort 37„ pytklaaloilthi

e*ctr.,-14 2. e)^rj cfr1/412..4 will toe...11000v/

56+.

Name: Date:

b. What is the probability of at least 2 being flawed? (2A,1C)

?Co) - PLC)

-.-_ , - C t )C0 os-Y( 0 •9 s-) c°I os-Y CO3 t S-) -

4.kno_r•e_ s. Q. 3. 27 7n c.haky.,ats

JA/t•i_k dk- \,,e1,-8-‘ 1.erv,3

c. What is the expected number of flawed engines? (1K,1C)

60;) = v'P (co•os-) o

clines of 6 gholA.Nok

be_ .00.,uf e2i

8. Jamaal has a success rate of 68% for scoring on free throws in basketball.

a. What is the probability that he will get a basket for the first time on his second throw? (2A,1C)

? 0 Jo cg

2.

X =

RA). (0.3z1 C0.4..53)

tc, of 2-1 ,*1370 chat/Ice IAA

IA) i ft coaskt.4 art h (.5

second 4-h rtw

b. What is the expected waiting time before he will get a basket? (1K,1C)

4,6 .cy etc-kd wat -h y,$) -1-01-uk 194-41r(-4--

,..°eks , bas Lei ,s s 0 0., ki_ 3V\CAA IA pssc+- ti• On

9. Explain the similarities and differences between the Binomial and Hyper-geometric distribution (4C) 4 " Pits PIO-

S\ S

bok-tIN ccAl -01" -PAO-- ac SU.C.C.e_sys

014-gff 404-Sn ' 4- neva( -Poi c

1)4v/was tStru,►4141 Is 1-6,, ,noteprotorir PA -1-s whk- t< 4 per 15 -Wyr ever►is

- 6 • 7 3s- --p.23 2_ 0 325f

-C)c _ 0. 32'o , y -/

Name: Date:

10. Suppose you randomly choose an integer, n, between 1 and 4, and then draw a circle with

a radius of n centimetres. What is the expected area of this circle to the nearest hundredth

of a square centimetre? (T:Out of Level 4)

A 7- 7

A =

A =

= teT

_ 30

3 s- (0 cr -■

-\-\(\k_ R-Y. T CA—esi e- th ■ s

2 S-10 CV11