Deck 5: Probability

Question 1

Which of the following statements is $\textbf{ not }$ 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.

Answer 1

probabilities are subjective measures with limited value in business.

Question 2

Probability is the basis for

A) quantitative data.
B) categorical data.
C) inferential statistics.
D) descriptive statistics.

Answer 2

inferential statistics.

Question 3

An event that $\textbf{ not }$ be broken down into other events is called a certainty outcome.

Answer 3

False

Question 4

The probability of A or 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 5

An experiment is a process that produces outcomes.

Question 6

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 7

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

Question 8

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

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 mutually exclusive.

Question 11

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 12

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 13

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

Question 14

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 15

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

Question 16

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

Question 17

If the occurrence of one event does $\textbf{ not }$ affect the occurrence of another event, then the two events are mutually exclusive.

Question 18

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 19

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 20

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 21

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) 15,625

Question 22

Which of the following is $\textbf{ not }$ a legitimate probability value?

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

Question 23

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 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}. F or 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 25

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 26

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 27

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 and 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 28

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 29

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 30

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 31

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 32

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 33

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 34

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 35

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 36

Which of the following is true regarding probability?
I: Probability is used by most industries.
II: By applying rules and laws one can conduct inferential process under uncertainty.

A) I only
B) II only
C) Both I and II
D) none of the above

Question 37

The department in which you work in your company has 24 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 38

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 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}. The complement of F is ___.

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

Question 40

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 41

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 42

Suppose that the probability that LIBOR (London inter-bank offered rate) will increase next trimester is 0.025. Assume also that the probability that your company will open a new branch overseas is 0.20. If the probability that at least one of the two events occur, i.e., LIBOR increases and/or your company opens a new overseas branch, is 0.21, what is the probability that both events occur?

A) 0.225
B) 0.015
C) 0.010
D) 0.007
E) 0.005

Question 43

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 44

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 45

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 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

Given P(A) = 0.40, P(B) = 0.50, P(A and B) = 0.15. Find P(A or B).

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

Question 48

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 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 or Electronics) = ___.

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

Question 50

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 51

The table below provides summary information about students in a class. The sex of each individual and their age range 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 52

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 53

Which of the following statements in $\textbf{ not }$ 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 54

Your company provides services to three different industries: automotive, construction, and financial services. These services can be either on a yearly or on a monthly contract. The cross-tabulation table below summarizes this information: If a client is randomly selected, what is the likelihood that it will be from the financial industry or on a monthly contract?

A) 26.6%
B) 42.3%
C) 51.8%
D) 65.5%
E) 67.5%

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 or F) = ___.

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

Question 56

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 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. 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 58

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 59

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 or E) = ___.

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

Question 60

The table below provides summary information about students in a class. The sex of each individual and their age range 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 61

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 62

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 63

Given P(A) = 0.45, P(B) = 0.30, P(A and B) = 0.05. Find P(B|A).

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

Question 64

The marketing department of your company is investigating the appeal of three possible service plans your company is planning to offer. The table below gives information obtained through a sample of 2395 clients. The three service plans are labelled A, B, and C. The clients are classified according to their industry and their service plan preference. If one of these consumers is randomly selected and prefers plan C, what is the probability that this client is from the construction industry?

A) 0.69
B) 0.68
C) 0.66
D) 0.60
E) 0.58

Question 65

The division of the company where you work has 85 employees. Thirty of them are bilingual, and 37% of the bilingual employees have a graduate degree. If an employee of this division is randomly selected, what is the probability that the employee is bilingual and has a graduate degree?

A) 0.130
B) 0.128
C) 0.126
D) 0.124
E) 0.122

Question 66

Define the following terms:
a) an experiment,
b) an event,
c) a sample space.

Question 67

What are the three methods of assigning probabilities?

Question 68

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 69

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?

Question 70

A recently published study shows that 50% of Americans adults take multivitamins regularly. Another recent study showed that 20.6% of American adults work out regularly. Suppose that these two variables are independent. The probability that a randomly selected American adult takes multivitamins regularly and works out regularly is ___.

A) 0.706
B) 0.309
C) 0.155
D) 0.106
E) 0.103

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.
Are "B" and "25 or older" independent and why or why $\textbf{ not? }$

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

Question 72

Name the branch of statistics that is supported by probability.

Question 73

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 74

Your company provides services to three different industries: automotive, construction, and financial services. These services can be either on a yearly or on a monthly contract. The cross-tabulation table below summarizes this information: Suppose you know that a given client is a construction company and you are interested in the likelihood that this client is on a yearly contract. This is an example of ___.

A) joint probability
B) marginal probability
C) conditional probability
D) a priori probability
E) a posteriori probability

Question 75

The table below provides summary information about students in a class. The sex of each individual and their age range 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 76

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 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 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 78

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 79

Given P(A) = 0.45, P(B) = 0.30, P(A and 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 80

Given P(A) = 0.45, P(B) = 0.30, P(A and B) = 0.05. Find P(A|B).

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