Deck 4: Probability

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

Probability is used to develop knowledge of the fundamental mathematical tools for quantitatively assessing risk.

Answer 3

True

Question 4

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 classical method.

Question 5

An experiment is a process that produces outcomes.

Question 6

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

Question 7

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

Question 8

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 9

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 10

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 11

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

Question 12

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

Question 13

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

Question 14

Given two events,A and B,if the probability of either A or B occurring is 0.6,then the probability of neither A nor B occurring is -0.6.

Question 15

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

Question 16

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

Question 17

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

Question 18

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 19

Given two events,A and B,if the probability of A is 0.7,the probability of B is 0.3,and the joint probability of A and B is 0.21,then the two events are independent.

Question 20

The probability of A $\cup$ B where A is receiving a state grant and B is receiving a federal grant is the probability of receiving no more than one of the two grants.

Question 21

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 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}.The complement of F is ___________.

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

Question 23

Which of the following is not a legitimate probability value?

A)0.87
B)12/13
C)0.05
D)5/4
E)0.93

Question 24

Let F be the event that a student is enrolled in afinance course,and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.Find the probability that a student is in finance and is also in statistics.

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

Question 25

Let F be the event that a student is enrolled in a finance course,and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.A student is randomly selected,what is the probability that the student is enrolled in either finance or statistics or both?

A)0.15
B)0.75
C)0.60
D)0.55
E)0.90

Question 26

In a set of 12 aluminum castings,two castings are defective (D),and the remaining ten are good (G).A quality control inspector randomly selects three of the twelve castings with replacement,and classifies each as defective (D)or good (G).The sample space for this experiment contains __________ elementary events.

A)1,728
B)220
C)120
D)10
E)66

Question 27

Which of the following statements is not true regarding probabilities: a.probability is the basis for inferential statistics
B.probabilities are subjective measures with limited value in business.
C.probabilities are used to determine the likelihood of certain outcomes
D.probabilities can inform many business decisions.

Question 28

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 29

Assigning probability 1/52 on drawing the ace of spade in a deck of cards 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 30

In a set of 25 aluminum castings,four castings are defective (D),and the remaining twenty-one are good (G).A quality control inspector randomly selects three of the twenty-five castings without replacement,and classifies each as defective (D)or good (G).The sample space for this experiment contains ____________ elementary events.

A)12,650
B)2,300
C)455
D)16
E)15,6255

Question 31

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 32

Which of the following statements in not true? a.the marginal probability uses the total possible outcomes in the denominator
B.the union probability is the probability of X or Y occurring.
C.the joint probability uses the probability of X in the denominator
D.the conditional probability uses subtotal of the possible outcomes in denominator

Question 33

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 34

If E and F are mutually exclusive,then _______.

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

Question 35

Which of the following is a legitimate probability value?

A)1.67
B)16/15
C)-0.23
D)3/2
E)0.28

Question 36

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 37

The number of different committees of 2 students that can be chosen from a group of 5 students is

A)20
B)2
C)5
D)10
E)1

Question 38

Let F be the event that a student is enrolled in a finance course,and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in an finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.Find P(S).

A)0.15
B)0.35
C)0.40
D)0.55
E)0.60

Question 39

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 40

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 41

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 labeled 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 42

The table below provides summary information about students in a class.The sex of each individual and their age 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 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 (Male)= ________

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

Question 44

Suppose 5% of the population have a certain disease.A laboratory blood test gives a positive reading for 95% of people who have the disease.What is the probability of testing positive and having the disease?

A)0.0475
B)0.95
C)0.05
D)0.9
E)0.02

Question 45

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 46

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 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

The table below provides summary information about students in a class.The sex of each individual and their age is given. If a student is randomly selected from this group,what is the probability that the student is a female who in under 20 years old?

A)0.08
B)0.18
C)0.52
D)0.26
E)0.78

Question 49

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 50

It is known that 20% of all students in some large university are overweight,20% exercise regularly and 2% are overweight and exercise regularly.What is the probability that a randomly selected student is either overweight or exercises regularly or both?

A)0.40
B)0.38
C)0.20
D)0.42
E)0.10

Question 51

Let F be the event that a student is enrolled in a finance course,and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.A student is randomly selected,and it is found that the student is enrolled in finance.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 52

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 53

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 54

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 55

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 56

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 labeled 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 57

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 58

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 59

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 60

Suppose that 3% of all TVs made by some Company in 2012 are defective.If 2 of these TVs are randomly selected what is the probability that both are defective?

A)0.0009
B)0.0025
C)0.0900
D)0.0475
E)0.19

Question 61

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 62

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 63

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 64

The table below provides summary information about students in a class.The sex of each individual and their age is given. A student is randomly selected from this group,and it is found that the student is older than 25 years.What is the probability that the student is a male?

A)0.21
B)0.10
C)0.50
D)0.54
E)0.26

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 labeled 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 66

It is known that 20% of all students in some large university are overweight,20% exercise regularly and 2% are overweight and exercise regularly.What is the probability that a randomly selected student is overweight given that this student exercises regularly?

A)0.40
B)0.38
C)0.20
D)0.42
E)0.10

Question 67

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 labeled 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 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 (H $\cap$ D')= ___________.

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

Question 69

Given P (A)= 0.45,P (B)= 0.30,P (A $\cap$ B)= 0.05.Find P (B|A).

A)0.45
B)0.135
C)0.30
D)0.111
E)0.167

Question 70

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 71

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 72

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 labeled 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 73

Given P (A)= 0.45,P (B)= 0.30,P (A $\cap$ B)= 0.05.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 74

Suppose 5% of the population have a certain disease.A laboratory blood test gives a positive reading for 95% of people who have the disease and 10% positive reading of people who do not have the disease..What is the probability of testing positive?

A)0.0475
B)0.1425
C)0.95
D)0.9
E)0.3333

Question 75

Suppose 5% of the population have a certain disease.A laboratory blood test gives a positive reading for 95% of people who have the disease and 10% positive reading of people who do not have the disease..What is the probability that a randomly selected person has the disease given that this person is testing positive?

A)0.0475
B)0.1425
C)0.95
D)0.9
E)0.3333

Question 76

Given P (A)= 0.45,P (B)= 0.30,P (A $\cap$ B)= 0.05.Find P (A|B).

A)0.45
B)0.135
C)0.30
D)0.111
E)0.167