Basic Probability And Discrete Probability Distributions
Chapter 5COUNTING TECHNIQUES AND PROBABILITY 2009 Statistical
Analysis. Session. 4 - # Statistics for Managers Using Microsoft
Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Basic Probability Concepts:Random ExperimentsSample
SpaceSample PointEventNull EventSimple EventCompound EventMutually
Exclusive Events/Disjoint EventsVenn Diagrams
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Random Experiment-Any process of generating a
set of data or observations that can be repeated under basically
the same conditions, which lead to well defined outcomes.-Any
process that can be repeated in which the results are
uncertain.
e.g. tossing a coin rolling a pair of dice drawing a card from a
deck
HeadTail
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Sample Space The set of all possible outcomes
of a statistical experiment and is represented by the symbol Se.g.
tossing a coin
HeadTailS = { H, T} 2 possible outcomes 2009 Statistical
Analysis. Session. 4 - # Statistics for Managers Using Microsoft
Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Sample Space Collection of all Possible Outcomes e.g. All 6
faces of a die:
e.g. All 52 cards of a bridge deck:
S = { 1, 2, 3, 4, 5, 6 } S = { all 52 cards } 2009 Statistical
Analysis. Session. 4 - # Statistics for Managers Using Microsoft
Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Sample Space Suppose that 3 items are selected at random
from a manufacturing process. Each item is inspected and classified
defective D, or non-defective N 2009 Statistical Analysis. Session.
4 - # Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Sample Space Suppose
that 3 items are selected at random from a manufacturing process.
Each item is inspected and classified defective D, or non-defective
N1st Item2nd Item3rd ItemSample
SpaceDNDNDNDNDNDNDNDDDDDNDNDDNNNDDNDNNNDNNNTree DiagramS = { DDD,
DDN, DND, DNN, NDD, NDN, NND, NNN } 2009 Statistical Analysis.
Session. 4 - # Statistics for Managers Using Microsoft Excel, 2/e
1999 Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Sample Space
Sample space with large or infinite number of sample points are
best described by a statement or ruleS = { x | x is a city with a
population over 1 million }ExampleS is the set of all x such that x
is a city with a population over 1 million 2009 Statistical
Analysis. Session. 4 - # Statistics for Managers Using Microsoft
Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Sample Space If S is the set of all points (x, y) on the
boundary of the circle of radius 2 centered at the origin.S = { (x
, y) | x2 + y2 = 4}r = 2 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Sample Point-An
element of the sample space.-An outcome.S = { 1, 2, 3, 4, 5 }
Sample points/outcomes 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#EventAn Event is a
subset of a sample space denoted by capital lettersS = { 1, 2, 3,
4, 5 } Event A= { 1, 3, 5 } Event B= { 2, 4 } Event C= { 5 } 2009
Statistical Analysis. Session. 4 - # Statistics for Managers Using
Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Events Simple Event: An event which contains only one
element in the sample space.e.g. Joint or Compound Event: An event
which can be expressed as a union of simple events, thus containing
more than one sample point.e.g.
Event C= { 5 } Event A= { 1, 3, 5 } Event B= { 2, 4 } 2009
Statistical Analysis. Session. 4 - # Statistics for Managers Using
Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Special Events Null Event Club & Diamond on 1 Card Draw
Complement of Event For Event A, All Events Not In A: ANull Event
2009 Statistical Analysis. Session. 4 - # Statistics for Managers
Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#We can combine events to form new events using
the various sets of operation
Is the event that occurs if A occurs or B occurs (or both) Is
the event that occurs if A occurs and B
The complement of A, is the event that occurs if A does not
occur.Operations With Events 2009 Statistical Analysis. Session. 4
- # Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Operations With
EventsIntersection of Events:The intersection of two events A and
B, denoted by the symbol A B , is the event containing all elements
that are common to A and B.
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Operations With EventsExample:Let A = { 1, 2,
3, 4, 5} and B={ 2, 4, 6, 8}; then
A B = ?
A B = { 2, 4}
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Operations With EventsExample:Let P = { a, e,
i, o, u} and Q = { r, s, t}; then
P Q = ?
P Q = { }=
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Operations With EventsMutually Exclusive
Events:Two events A and B are mutually exclusive if A B = : that is
A and B have no elements in common.
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Two events A and B are called mutually
exclusive if they are disjointEvent AEvent B
Operations With Events 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Operations With
EventsExample (Mutually Exclusive Events):
Supposed that a die is tossed. Let A be the event that an even
number turns up and B the event that an odd number shows. A B = A =
{ 2, 4, 6} and B= { 1, 3, 5}Events A and B are mutually exclusive
2009 Statistical Analysis. Session. 4 - # Statistics for Managers
Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Operations With EventsUnion of Events:The union
of two events A and B, denoted by the symbol A U B , is the event
containing all elements that belongs to A or to B or to both 2009
Statistical Analysis. Session. 4 - # Statistics for Managers Using
Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Operations With EventsUnion of Events:ExampleLet A = { 2,
3, 5, 8} and B={ 3, 6, 8}; then
A U B = ?
A U B = { 2, 3, 5, 6, 8} 2009 Statistical Analysis. Session. 4 -
# Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Operations With
EventsUnion of Events:ExampleLet M = {x | 3 < x < 9} and N =
{y | 5 < y < 12}then
M U N = ?
M U N = {z | 3 < z < 12} 2009 Statistical Analysis.
Session. 4 - # Statistics for Managers Using Microsoft Excel, 2/e
1999 Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Operations With
EventsComplement of an Event:The complement of an event A with
respect to S is the set of all elements of S that are not in A. We
denote the complement of A by the symbol A. 2009 Statistical
Analysis. Session. 4 - # Statistics for Managers Using Microsoft
Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Operations With EventsComplement of an Event:Example Let R
be the event that a red card is selected from an ordinary deck of
52 playing cards and let S be the entire deck. R = event that the
card selected from the deck is not red but a black card 2009
Statistical Analysis. Session. 4 - # Statistics for Managers Using
Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Counting Sample PointsMultiplication Rule:If an operation
can be performed in n1 ways, and for each of these a second
operation can be performed in n2 ways, then two operations can be
performed together in n1n2 ways
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Counting Sample PointsMultiplication
Rule:Example How many sample points are in the sample space when a
pair of dice is thrown once? 2009 Statistical Analysis. Session. 4
- # Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Counting Sample
PointsMultiplication Rule:Example How many sample points are in the
sample space when a pair of dice is thrown once?Solution1st die 6
ways2nd die 6 ways (6)(6) = 36 ways 2009 Statistical Analysis.
Session. 4 - # Statistics for Managers Using Microsoft Excel, 2/e
1999 Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Counting Sample
PointsGeneralized Multiplication Rule:If an operation can be
performed in n1 ways, and for each of these a second operation can
be performed in n2 ways, if for each of the first two a third
operation can be performed in n3 ways, and so on, then the sequence
of k operations can be performed in n1n2..nk ways 2009 Statistical
Analysis. Session. 4 - # Statistics for Managers Using Microsoft
Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Counting Sample PointsGeneralized Multiplication
Rule:Example How many lunches are possible consisting of soup, a
sandwich, dessert, and a drink if one can select from 4 soups, 3
kinds of sandwiches, 5 deserts, and 4 drinks? 2009 Statistical
Analysis. Session. 4 - # Statistics for Managers Using Microsoft
Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Counting Sample PointsGeneralized Multiplication
Rule:Example How many lunches are possible consisting of soup, a
sandwich, dessert, and a drink if one can select from 4 soups, 3
kinds of sandwiches, 5 deserts, and 4 drinks?Solution (4)(3)(5)(4)
= 240 lunches 2009 Statistical Analysis. Session. 4 - # Statistics
for Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall,
Inc.Chapter 4Instructor Notes4-#Counting Sample PointsGeneralized
Multiplication Rule:Example How many even three-digit numbers can
be formed from the digits 1, 2, 5, 6 and 9. if each digit can be
used only once? 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Counting Sample
PointsGeneralized Multiplication Rule:Example How many even
three-digit numbers can be formed from the digits 1, 2, 5, 6 and 9.
if each digit can be used only once?Solution (2)(4)(3) = 24 even
three-digit numbers 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Counting Sample
PointsPERMUTATION:A Permutation is an arrangement of all or part of
a set of objects.
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Counting Sample PointsTheorem 1The number of
permutations of n distinct objects is n!Permutation: 2009
Statistical Analysis. Session. 4 - # Statistics for Managers Using
Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Counting Sample PointsPermutation:Consider the three
letters, a, b, cPossible permutations are:abc, acb, bac, bca, cab,
cbaExample 2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Counting Sample PointsExampleThe number of
permutations of the four letters a, b, c, and d4! = (4)(3)(2)(1) =
24 2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Counting Sample PointsTheorem 2The number of
permutations of n distinct objects taken r at a time is
Permutation: 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Counting Sample
PointsExample 1The number of permutations of the four letters a, b,
c, and d taken 2 at a timeab, ac, ad, bc, bd, ba, cd, ca, cb, da,
db, dc(4)(3) = 12 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Counting Sample
PointsExample 2Two lottery tickets are drawn from 20 for the first
and second prizes. Find the number of sample points in the space S.
2009 Statistical Analysis. Session. 4 - # Statistics for Managers
Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Counting Sample PointsExample
Two lottery tickets are drawn from 20 for the first and second
prizes. Find the number of sample points in the space S.
Solution
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Counting Sample PointsTheorem 3The number of
permutations of n distinct objects arranged in a circle is
Permutation: 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Counting Sample
PointsTheorem 3Example: In how many ways can Cale, Anna, Jen, and
Karla be arranged in a circular table?Solution:
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Counting Sample PointsTheorem 4 The number of
distinct permutations of n things of which n1 are of one kind, n2
of a second kind .. nk of kth kind is
Permutation: 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Counting Sample
PointsExampleHow many different ways can 3 red, 4 yellow, and 2
blue bulbs be arranged in a string of Christmas tree lights with 9
sockets? 2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Counting Sample PointsExampleHow many different
ways can 3 red, 4 yellow, and 2 blue bulbs be arranged in a string
of Christmas tree lights with 9 sockets?Solution
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Counting Sample PointsCOMBINATIONThe number of
combinations of n objects taken r at a time is
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Counting Sample PointsExample 1Je, Roy, Fe, and
Al are going to play golf. They will randomly select teams of two
players each.
a. How many team combinations are possible?b. List them. 2009
Statistical Analysis. Session. 4 - # Statistics for Managers Using
Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#Counting Sample PointsExample 2From 4 Republicans and 3
Democrats find the number of committees of 3 that can be formed
with 2 republicans and 1 Democrats? 2009 Statistical Analysis.
Session. 4 - # Statistics for Managers Using Microsoft Excel, 2/e
1999 Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Counting Sample
PointsExampleFrom 4 Republicans and 3 Democrats find the number of
committees of 3 that can be formed with 2 republicans and 1
Democrats?Solution
RepublicansDemocrats
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#PROBABILITYProbability is the numerical measure
of the likelihood that the event will occur.Value is between 0 and
1.Sum of the probabilities of all mutually exclusive events is
1.CertainImpossible.510 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#As the number of
repetitions of a probability experiment increases, the proportion
with which a certain outcome is observed gets closer to the
probability of the outcome.
The Law of Large Numbers 2009 Statistical Analysis. Session. 4 -
# Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#Historically,
Probability began with the study of games of chance
The probability p on event Ap =P(A) = n(S)n(A)If A can occur in
n(A) ways out of a total of n(S) equally likely ways,
thenProbability 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#If an experiment can
result in any one of n(S) different equally likely outcomes and if
exactly n(A) of these outcomes correspond to event A, then the
probability of event A is
Computing Probability Using Classical Approach (Assuming Equally
Likely Outcomes) 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#The study of random
or nondeterministic experimentsComputing Probability using Relative
Frequency Approach
Let s = number of successes Let n = number of tossesnsf =
relative frequency stable in the long run basis of probability
theory 2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Example, in tossing a die an even number can
occur 3 ways out of 6 equally likely ways P = 63 = 21Probability 3
even numbers 2009 Statistical Analysis. Session. 4 - # Statistics
for Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall,
Inc.Chapter 4Instructor Notes4-#Let E be any event, S be the sample
space, and be a null event,0 P(E) 1 P( ) =0 P( S) = 1 If S = { e1,
e2,en} =P(e1)+P(e2)++P(en) =P(S)=1
PROPERTIES OF PROBABILITY 2009 Statistical Analysis. Session. 4
- # Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#ExampleA coin is
tossed twice. What is the probability that at least 1 head
occurs?Computing Probability 2009 Statistical Analysis. Session. 4
- # Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#ExampleA coin is
tossed twice. What is the probability that at least 1 head
occurs?Computing Probability
SolutionS={HH, HT, TH, TT}
A={at least 1 head}A={HH, HT, TH }P(A)= + + =
3/41w1w1w1wP(S)=1,P(S)=4w w = 1/4 2009 Statistical Analysis.
Session. 4 - # Statistics for Managers Using Microsoft Excel, 2/e
1999 Prentice-Hall, Inc.Chapter 4Instructor Notes4-#ExampleIf a
card is drawn from an ordinary deck, find the probability that it
is a heartComputing Probability 2009 Statistical Analysis. Session.
4 - # Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#ExampleIf a card is
drawn from an ordinary deck, find the probability that it is a
heartComputing ProbabilitySolutionS={52 cards}, n(S)=52A={heart}, n
(A)= 13
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#ExampleIn a poker hand consisting 5 cards, find
the probability of holding 2 aces and 3 jacks.Computing Probability
2009 Statistical Analysis. Session. 4 - # Statistics for Managers
Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#ExampleIn a poker hand consisting 5 cards, find
the probability of holding 2 aces and 3 jacks.Computing
ProbabilitySolution
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Theorem 4.10 (Additive Rule)If A and B are any
two events, then
Computing ProbabilityIf A and B are mutually exclusive, then
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Theorem 4.10 (Additive Rule) continuedIf A1,
A2, .. Ak are mutually exclusive, then
Computing Probability 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#ExampleThe
probability that a student passes mathematics is 2/3, and the
probability that he passes English is 4/9. If the probability of
passing at least one course is 4/5, what is the probability that he
will pass both courses?Computing Probability 2009 Statistical
Analysis. Session. 4 - # Statistics for Managers Using Microsoft
Excel, 2/e 1999 Prentice-Hall, Inc.Chapter 4Instructor
Notes4-#ExampleThe probability that a student passes mathematics is
2/3, and the probability that he passes English is 4/9. If the
probability of passing at least one course is 4/5, what is the
probability that he will pass both courses?Computing
ProbabilitySolution
Given:Additive Rule: 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#ExampleWhat is the
probability of getting a total of 7 or 11 when a pair of dice is
tossed?Computing Probability 2009 Statistical Analysis. Session. 4
- # Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#ExampleWhat is the
probability of getting a total of 7 or 11 when a pair of dice is
tossed?Computing ProbabilitySolution
P(A) = getting a total of 7 P(B) = getting a total of 11
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#Theorem 4.11 If A and A are complementary
events, then
Computing Probability 2009 Statistical Analysis. Session. 4 - #
Statistics for Managers Using Microsoft Excel, 2/e 1999
Prentice-Hall, Inc.Chapter 4Instructor Notes4-#ExampleA coin is
tossed 6 times in succession. What is the probability that at least
1 head occurs?Computing Probability 2009 Statistical Analysis.
Session. 4 - # Statistics for Managers Using Microsoft Excel, 2/e
1999 Prentice-Hall, Inc.Chapter 4Instructor Notes4-#ExampleA coin
is tossed 6 times in succession. What is the probability that at
least 1 head occurs?Computing ProbabilitySolutionLet E = {at least
1 head}N = (2)(2)(2)(2)(2)(2) = 26=64E = {no head} = {TTTTTT}
P(E) = 1/64
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#SummaryDiscussed Basic Probability
Concepts:Sample Spaces and Events, Counting Sample Points, Simple
Probability
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#According to the Filipino Veterinary
Association, 31.6% of the Filipino households own a dog. What is
the probability that a randomly selected household does not own a
dog?
2. A newly wed couple is choosing where they would spend their
honeymoon. Due to the peak season, the probability that they can
book to a hotel in Palawan is 0.45 and to Boracay is 0.4 and the
probability that they can book a hotel in both places is 0.3. What
is the probability that they can book to a hotel in Palawan or
Boracay?
3. If 3 books are picked at random from a shelf containing 5
novels, 3 books of poems, and a dictionary, what is the probability
thata) The dictionary is selectedb) 2 novels and 1 book of poems
are selected?
What is the probability that they can book to a hotel in Palawan
or Boracay?
ASSIGNMENT:6. A 5-sided die with sides numbered 1, 2, 3, 4, and
5 is constructed so that the 1 and 5 occur twice as often as the 2
and 4, which occur three times as often as the 3. What is the
probability that a perfect square occurs when this die is tossed
once?
2009 Statistical Analysis. Session. 4 - # Statistics for
Managers Using Microsoft Excel, 2/e 1999 Prentice-Hall, Inc.Chapter
4Instructor Notes4-#
