Deck 4: Probability

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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.

Answer 3

False

Question 4

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 5

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 6

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 7

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 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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 14

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

Question 15

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 16

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

Question 17

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 18

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

Question 19

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 20

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

Question 21

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 22

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 23

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 24

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 25

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 26

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 27

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 28

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 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 $\cup$ 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 30

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 31

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 32

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 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}. The complement of F is ___________.

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

Question 34

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 35

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 36

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 37

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 38

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 39

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 40

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 41

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 42

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 43

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 44

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 45

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 46

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

Question 47

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 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

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 51

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 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 $\cup$ E)= _____________.

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

Question 53

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 54

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 55

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 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

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 58

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 59

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 60

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 61

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 62

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 63

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 64

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 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. 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

Suppose that your company is sending invitations to its 50 most important clients for an end-of-the-year event where a new product will be exhibited.These are printed invitation cards mailed through USPS,and each card is personalized with the name of the corresponding client.You realize that the cards have been accidentally shuffled before placing them in the envelopes.What is the probability that only one card is in the wrong envelope?

A) 0.02
B) 0.15
C) 0.10
D) 0.05
E) 0.00

Question 67

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 68

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 69

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 70

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 71

The department in which you work in your company has 24 employees.A team of 3 employees must be selected to represent the department at a companywide meeting in the headquarters of the company.How many different teams of 3 can be selected?

A) 3
B) 8
C) 24
D) 72
E) 2024

Question 72

The department in which you work in your company has 10 employees: 10 women and 14 men.A team of anywhere from one employee up to 9 employees must be chose to attend a meeting at the company's headquarters.How many different teams can be selected?

A) 1024
B) 1023
C) 1022
D) 1021
E) 1020

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

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 75

Suppose you toss a fair coin three times in a row and obtain tails,tails,and tails.What it the probability that the fourth toss will give heads?

A) 0.75
B) 0.67
C) 0.50
D) 0.33
E) 0.25

Question 76

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 77

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 78

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 79

The department in which you work in your company has 24 employees: 10 women and 14 men.A team of 4 employees must be selected to represent the department at a companywide meeting in the headquarters of the company.The team must have two women and two men.How many different teams of 4 can be selected?

A) 12
B) 35
C) 136
D) 2024
E) 4095

Question 80

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