Deck 4: Probability

Question 1

Calculate conditional probabilities with various forms of the law of conditional probability,and use them to determine if two events are independent.

Answer 1

The general law of addition is used when we need to find the probability of the union of two events (X or Y or both occurring).The general law of multiplication is used to find the probability of two events X and Y happening together (joint probability).Conditional probabilities are used when we want to incorporate prior knowledge one may have regarding the two events studied.

Question 2

If two events are mutually exclusive,then their joint probability is always zero.

Answer 2

True

Question 3

Describe what probability is and when one would use it.

Answer 3

The study of probability addresses ways of assigning probabilities,types of probabilities,and laws of probabilities.Probabilities support the notion of inferential statistics.Using sample data to estimate and test hypotheses about population parameters is done with uncertainty.If samples are taken at random,probabilities can be assigned to outcomes of the inferential process.

Question 4

The method of assigning probabilities to uncertain outcomes based on laws and rules is called the classical method.

Question 5

Deconstruct the elements of probability by defining experiments,sample spaces,and events;classifying events as mutually exclusive,collectively exhaustive,complementary,or independent;and counting possibilities.

Question 6

Calculate probabilities using the general law of addition,along with a joint probability table,the complement of a union,or the special law of addition if necessary.

Question 7

Given two events,A and B,if the probability of either A or B occurring is 0.8,then the probability of neither A nor B occurring is -0.8.

Question 8

An event that cannot be broken down into other events is called a certainty outcome.

Question 9

If two events are mutually exclusive,then the two events are also independent.

Question 10

If the occurrence of one event precludes the occurrence of another event,then the two events are independent.

Question 11

Compare marginal,union,joint,and conditional probabilities by defining each one.

Question 12

The list of all elementary events for an experiment is called the sample space.

Question 13

Assigning probabilities by dividing the number of ways that an event can occur by the total number of possible outcomes in an experiment is called the relative frequency of occurrence method.

Question 14

Calculate conditional probabilities using Bayes' rule.

Question 15

If the occurrence of one event does not affect the occurrence of another event,then the two events are mutually exclusive.

Question 16

Differentiate among three methods of assigning probabilities: the classical method,relative frequency of occurrence,and subjective probability.

Question 17

Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

Question 18

An experiment is a process that produces outcomes.

Question 19

Inferring the value of a population parameter from the statistic on a random sample drawn from the population is an inferential process under uncertainty.

Question 20

Assigning probabilities to uncertain events based on one's beliefs or intuitions is called classical method.

Question 21

Which of the following is not a legitimate probability value?

A)0.67
B)15/16
C)0.23
D)2/3
E)-0.28

Question 22

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.F $\cup$ H is ___.

A){Meagan}
B){Betty,Abel,Patty,Meagan}
C)empty,since F and H are complements
D)empty,since F and H are independent
E)empty,since F and H are mutually exclusive

Question 23

Given that two events,A and B,are independent,if the marginal probability of A is 0.6,the conditional probability of A given B will be 0.4.

Question 24

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.The complement of F is ___.

A){Albert,Betty,Jack,Patty}
B){Betty,Patty,Meagan}
C){Albert,Abel,Jack}
D){Betty,Abel}
E){Meagan}

Question 25

Belinda Bose is reviewing a newly proposed advertising campaign.Based on her 15 years experience,she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product.This is an example of assigning probabilities using the ___ method.

A)subjective probability
B)relative frequency
C)classical probability
D)a priori probability
E)a posterior probability

Question 26

Given two events A and B each with a non-zero probability,if the conditional probability of A given B is zero,it implies that the events A and B are independent.

Question 27

Bayes' rule is a rule to assign probabilities under the classical method.

Question 28

The list of all elementary events for an experiment is called ___.

A)the sample space
B)the exhaustive list
C)the population space
D)the event union
E)a frame

Question 29

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.F $\cap$ H is ___.

A){Meagan}
B){Betty,Patty,Abel,Meagan}
C)empty,since F and H are complements
D)empty,since F and H are independent
E)empty,since F and H are mutually exclusive

Question 30

If X and Y are mutually exclusive events,then if X occurs,___.

A)Y must also occur
B)Y cannot occur
C)X and Y are independent
D)X and Y are complements
E)A and Y are collectively exhaustive

Question 31

Let A be the event that a student is enrolled in an accounting course,and let S be the event that a student is enrolled in a statistics course.It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and accounting.A student is randomly selected,and it is found that the student is enrolled in accounting.What is the probability that this student is also enrolled in statistics?

A)0.15
B)0.75
C)0.375
D)0.50
E)0.80

Question 32

Bayes' rule is an extension of the law of conditional probabilities to allow revision of original probabilities with new information.

Question 33

Which of the following is not a legitimate probability value?

A)0.67
B)15/16
C)0.23
D)4/3
E)0.98

Question 34

Given two events A and B each with a non-zero probability,if the conditional probability of A given B is zero,it implies that the events A and B are mutually exclusive.

Question 35

Given two events,A and B,if the probability of A is 0.6,the probability of B is 0.4,and the joint probability of A and B is 0.24,then the two events are independent.

Question 36

Let A be the event that a student is enrolled in an accounting course,and let S be the event that a student is enrolled in a statistics course.It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and accounting.Find P(S).

A)0.15
B)0.30
C)0.40
D)0.55
E)0.60

Question 37

If X and Y are mutually exclusive,then ___.

A)the probability of the union is zero
B)P(X)= 1 - P(Y)
C)the probability of the intersection is zero
D)the probability of the union is one
E)P(Y)= P(X)

Question 38

In a set of 15 aluminum castings,two castings are defective (D),and the remaining thirteen are good (G).A quality control inspector randomly selects three of the fifteen castings without replacement,and classifies each as defective (D)or good (G).The sample space for this experiment contains ___ elementary events.

A)3,375
B)2,730
C)455
D)15
E)3

Question 39

In a set of 10 aluminum castings,two castings are defective (D),and the remaining eight are good (G).A quality control inspector randomly selects three of the ten castings with replacement,and classifies each as defective (D)or good (G).The sample space for this experiment contains ___ elementary events.

A)1,000
B)720
C)100
D)10
E)3

Question 40

Let A be the event that a student is enrolled in an accounting course,and let S be the event that a student is enrolled in a statistics course.It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and accounting.Find the probability that a student is in accounting and is also in statistics.

A)0.15
B)0.70
C)0.55
D)0.12
E)0.60

Question 41

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the following joint probability table that was developed from the dealer's records for the previous year,P (Male)= ___.

A)0.48
B)0.50
C)0.20
D)0.02
E)0.60

Question 42

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' If a stock is selected randomly from Meagan's portfolio,P (Growth)= ___.

A)0.50
B)0.83
C)0.67
D)0.75
E)0.90

Question 43

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the following joint probability table that was developed from the dealer's records for the previous year,P (SUV)= ___.

A)0.30
B)0.40
C)0.12
D)0.10
E)0.60

Question 44

Given P (A)= 0.40,P (B)= 0.50,P (A $\cap$ 0 B)= 0.15.Find P (A|B).

A)0.20
B)0.80
C)0.30
D)0.375
E)0.15

Question 45

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the joint probability table below that was developed from the dealer's records for the previous year,P (Female $\cap$ SUV)= ___.

A)0.30
B)0.40
C)0.12
D)0.10
E)0.60

Question 46

Abel Alonzo,Director of Human Resources,is exploring employee absenteeism at the Plano Power Plant.Ten percent of all plant employees work in the finishing department;20% of all plant employees are absent excessively;and 7% of all plant employees work in the finishing department and are absent excessively.A plant employee is selected randomly;F is the event "works in the finishing department;" and A is the event "is absent excessively." P(A|F)= __.

A)0.37
B)0.70
C)0.13
D)0.35
E)0.80

Question 47

Abel Alonzo,Director of Human Resources,is exploring employee absenteeism at the Plano Power Plant.Ten percent of all plant employees work in the finishing department;20% of all plant employees are absent excessively;and 7% of all plant employees work in the finishing department and are absent excessively.A plant employee is selected randomly;F is the event "works in the finishing department;" and A is the event "is absent excessively." P(A $\cup$ F)= ___.

A)0.07
B)0.10
C)0.20
D)0.23
E)0.37

Question 48

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' Which of the following statements is true?

A)Growth and Healthcare are complementary events.
B)Electronics and Growth are independent.
C)Electronics and Growth are mutually exclusive.
D)Airlines and Healthcare are collectively exhaustive.
E)Electronics and Healthcare are collectively exhaustive.

Question 49

Max Sandlin is exploring the characteristics of stock market investors.He found that sixty percent of all investors have a net worth exceeding $1,000,000;20% of all investors use an online brokerage;and 10% of all investors a have net worth exceeding $1,000,000 and use an online brokerage.An investor is selected randomly,and E is the event "net worth exceeds $1,000,000," and O is the event "uses an online brokerage." P(O|E)= ___.

A)0.17
B)0.50
C)0.80
D)0.70
E)0.88

Question 50

Abel Alonzo,Director of Human Resources,is exploring employee absenteeism at the Plano Power Plant.Ten percent of all plant employees work in the finishing department;20% of all plant employees are absent excessively;and 7% of all plant employees work in the finishing department and are absent excessively.A plant employee is selected randomly;F is the event "works in the finishing department;" and A is the event "is absent excessively." P(F|A)= ___.

A)0.35
B)0.70
C)0.13
D)0.37
E)0.10

Question 51

Let A be the event that a student is enrolled in an accounting course,and let S be the event that a student is enrolled in a statistics course.It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and accounting.A student is randomly selected,what is the probability that the student is enrolled in either accounting or statistics or both?

A)0.15
B)0.85
C)0.70
D)0.55
E)0.90

Question 52

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.'
If a stock is selected randomly from Meagan's portfolio,P (Healthcare $\cup$ Electronics)= ___.

A)0.25
B)0.85
C)0.60
D)0.75
E)0.90

Question 53

Given P (A)= 0.40,P (B)= 0.50,P (A $\cap$ B)= 0.15.Find P (B|A).

A)0.20
B)0.80
C)0.30
D)0.375
E)0.15

Question 54

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' Which of the following statements is not true?

A)Growth and Income are complementary events.
B)Electronics and Growth are dependent.
C)Electronics and Healthcare are mutually exclusive.
D)Airlines and Healthcare are collectively exhaustive.
E)Growth and Income are collectively exhaustive.

Question 55

Given P(A)= 0.40,P(B)= 0.50,P(A $\cap$ B)= 0.15.Find P(A $\cup$ B).

A)0.90
B)1.05
C)0.75
D)0.65
E)0.60

Question 56

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' If a stock is selected randomly from Meagan's portfolio,P (Airlines|Income)= ___.

A)0.10
B)0.40
C)0.25
D)0.67
E)0.90

Question 57

Given P (A)= 0.40,P (B)= 0.50,P (A $\cap$ B)= 0.15.Which of the following is true?

A)A and B are independent.
B)A and B are mutually exclusive.
C)A and B are collectively exhaustive.
D)A and B are not independent.
E)A and B are complimentary.

Question 58

The table below provides summary information about students in a class.The sex of each individual and the major is given. If a student is randomly selected from this group,what is the probability that the student is male?

A)0.12
B)0.48
C)0.50
D)0.52
E)0.68

Question 59

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the following joint probability table that was developed from the dealer's records for the previous year,P (Female)= ___.

A)0.30
B)0.40
C)0.12
D)0.10
E)0.60

Question 60

Max Sandlin is exploring the characteristics of stock market investors.He found that sixty percent of all investors have a net worth exceeding $1,000,000;20% of all investors use an online brokerage;and 10% of all investors a have net worth exceeding $1,000,000 and use an online brokerage.An investor is selected randomly,and E is the event "net worth exceeds $1,000,000" and O is the event "uses an online brokerage." P(O $\cup$ E)= ___.

A)0.17
B)0.50
C)0.80
D)0.70
E)0.10

Question 61

A market research firms conducts studies regarding the success of new products.The company is not always perfect in predicting the success.Suppose that there is a 50% chance that any new product would be successful (and a 50% chance that it would fail).In the past,for all new products that ultimately were successful,80% were predicted to be successful (and the other 20% were inaccurately predicted to be failures).Also,for all new products that were ultimately failures,70% were predicted to be failures (and the other 30% were inaccurately predicted to be successes).For any randomly selected new product,what is the probability that the market research firm would predict that it would be a success?

A)0.80
B)0.50
C)0.45
D)0.55
E)0.95

Question 62

A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labelled A,B,and C.The consumers are classified according to age and package design preference. If one of these consumers is randomly selected and is under 25,what is the probability that the person prefers design A?

A)0.22
B)0.23
C)0.29
D)0.18
E)0.78

Question 63

A market research firms conducts studies regarding the success of new products.The company is not always perfect in predicting the success.Suppose that there is a 50% chance that any new product would be successful (and a 50% chance that it would fail).In the past,for all new products that ultimately were successful,80% were predicted to be successful (and the other 20% were inaccurately predicted to be failures).Also,for all new products that were ultimately failures,70% were predicted to be failures (and the other 30% were inaccurately predicted to be successes).What is the a priori probability that a new product would be a success?

A)0.50
B)0.80
C)0.70
D)0.60
E)0.95

Question 64

A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labelled A,B,and C.The consumers are classified according to age and package design preference. If one of these consumers is randomly selected,what is the probability that the person prefers design A?

A)0.76
B)0.38
C)0.33
D)0.22
E)0.39

Question 65

A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labelled A,B,and C.The consumers are classified according to age and package design preference. If one of these consumers is randomly selected and prefers design B,what is the probability that the person is 25 or older?

A)0.28
B)0.14
C)0.45
D)0.27
E)0.78

Question 66

The table below provides summary information about students in a class.The sex of each individual and the major is given. If a student is randomly selected from this group,what is the probability that the student is a female who majors in accounting?

A)0.18
B)0.60
C)0.35
D)0.40
E)0.78

Question 67

A market research firm conducts studies regarding the success of new products.The company is not always perfect in predicting the success.Suppose that there is a 50% chance that any new product would be successful (and a 50% chance that it would fail).In the past,for all new products that ultimately were successful,80% were predicted to be successful (and the other 20% were inaccurately predicted to be failures).Also,for all new products that were ultimately failures,70% were predicted to be failures (and the other 30% were inaccurately predicted to be successes).If the market research predicted that the product would be a success,what is the probability that it would actually be a success?

A)0.27
B)0.73
C)0.80
D)0.24
E)1.00

Question 68

An analysis of personal loans at a local bank revealed the following facts: 10% of all personal loans are in default (D),90% of all personal loans are not in default (D΄),20% of those in default are homeowners (H | D),and 70% of those not in default are homeowners (H | D΄).If a personal loan is selected at random,P (D | H)= ___.

A)0.03
B)0.63
C)0.02
D)0.18
E)0.78

Question 69

An analysis of personal loans at a local bank revealed the following facts: 10% of all personal loans are in default (D),90% of all personal loans are not in default (D΄),20% of those in default are homeowners (H | D),and 70% of those not in default are homeowners (H | D΄).If a personal loan is selected at random P (H $\cap$ D')= ___.

A)0.20
B)0.63
C)0.90
D)0.18
E)0.78

Question 70

A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labelled A,B,and C.The consumers are classified according to age and package design preference. Are "B" and "25 or older" independent and why or why not?

A)No,because P (25 or over | B) $\neq$ P (B).
B)Yes,because P (B)= P(C).
C)No,because P (25 or older | B) $\neq$ P (25 or older).
D)Yes,because P (25 or older $\cap$ B) $\neq$ 0.
E)No,because age and package design are different things.

Question 71

A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labelled A,B,and C.The consumers are classified according to age and package design preference. If one of these consumers is randomly selected,what is the probability that the person prefers design A and is under 25?

A)0.22
B)0.11
C)0.18
D)0.54
E)0.78

Question 72

The table below provides summary information about students in a class.The gender of each individual and the major is given. A student is randomly selected from this group,and it is found that the student is majoring in finance.What is the probability that the student is a male?

A)0.21
B)0.10
C)0.56
D)0.48
E)0.78