Test Bank Docx Chapter 4 Probability

File: ch04, Chapter 4: Probability

True/false

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

Response: See section 4.1 Introduction to Probability

Difficulty: Easy

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

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

Response: See section 4.1 Introduction to Probability

Difficulty: Easy

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

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

Response: See section 4.1 Introduction to Probability

Difficulty: Easy

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

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.

Response: See section 4.1 Introduction to Probability

Difficulty: Easy

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

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

Response: See section 4.1 Introduction to Probability

Difficulty: Easy

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

6. An experiment is a process that produces outcomes.

Response: See section 4.2 Structure of Probability

Difficulty: Easy

Learning Objective: 4.2: 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.

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

Response: See section 4.2 Structure of Probability

Difficulty: Easy

Learning Objective: 4.2: 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.

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

Response: See section 4.2 Structure of Probability

Difficulty: Easy

Learning Objective: 4.2: 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.

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

Response: See section 4.2 Structure of Probability

Difficulty: Medium

Learning Objective: 4.2: 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.

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

Response: See section 4.2 Structure of Probability

Difficulty: Medium

Learning Objective: 4.2: 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.

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

Response: See section 4.2 Structure of Probability

Difficulty: Hard

Learning Objective: 4.2: 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.

12. The probability of A ∪ 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.

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Easy

Learning Objective: 4.3: Compare marginal, union, joint, and conditional probabilities by defining each one.

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

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Medium

Learning Objective: 4.3: compare marginal, union, joint,, and conditional probabilities by defining each one.

14. The probability that a person’s favorite color is blue would be an example of a marginal probability.

Ans: True

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Medium

Learning Objective: 4.3: compare marginal, union, joint,, and conditional probabilities by defining each one.

15. A joint probability is the probability that at least one of two events occurs.

Ans: False

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Medium

Learning Objective: 4.3: compare marginal, union, joint,, and conditional probabilities by defining each one.

16. In the conditional probability of P(E₁|E₂) is when E₂ has occurred and then the probability of E₁ occurring is determined.

Ans: True

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Medium

Learning Objective: 4.3: compare marginal, union, joint,, and conditional probabilities by defining each one.

17. 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.

Response: See section 4.4 Addition Laws

Difficulty: Easy

Learning Objective: 4.4: 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.

18. 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.

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

19. The law of multiplication gives the probability that at least one of the two events will occur.

Ans: False

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

20. If the probability that someone likes the color blue is 44% and the probability that among those individuals, the probability that they wake up early is 52%, then the probability that individuals who like the color blue and wake up early is about 23%.

Ans: True

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

21. If the probability that someone likes the color blue is 44% and the probability that individuals wake up early is 64%, then the probability that individuals who like the color blue and wake up early is about 23%. In this case, the two events are independent.

Ans: False

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

22. If P(X|Y) = P(X) then the events are X and Y are independent.

Ans: True

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

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.

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent.

24. 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.

Response: See section 4.6 Conditional Probability

Difficulty: Hard

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent

25. 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.

Response: See section 4.6 Conditional Probability

Difficulty: Hard

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent.

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

Response: See section 4.7 Revision of Probabilities: Bayes’ Rule

Difficulty: Easy

Learning Objective: 4.7: Calculate conditional probabilities using Bayes’ rule.

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

Response: See section 4.7 Revision of Probabilities: Bayes’ Rule

Difficulty: Easy

Learning Objective: 4.7: Calculate conditional probabilities using Bayes’ rule.

Multiple Choice

28. 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.

Response: See section 4.1 Introduction to Probability

Difficulty: Easy

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

29. 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

Response: See section 4.1 Introduction to Probability

Difficulty: Medium

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

30. 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

Response: See section 4.1 Introduction to Probability

Difficulty: Easy

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

31. Which of the following is a legitimate probability value?

a) 1.67

b) 16/15

c) -0.23

d) 3/2

e) 0.28

Response: See section 4.1 Introduction to Probability

Difficulty: Easy

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

32. 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

Response: See section 4.1 Introduction to Probability

Difficulty: Medium

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

33. 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

Response: See section 4.2 Structure of Probability

Difficulty: Easy

Learning Objective: 4.2: 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.

34. 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, to test. The sample space for selecting the group to test contains ____________ elementary events.

a) 12,650

b) 2,300

c) 455

d) 16

e) 15,625

Response: See section 4.2 Structure of Probability

Difficulty: Medium

Learning Objective: 4.2: 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.

35. 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 to test. The sample space for selecting the group to test contains __________ elementary events.

a) 8

b) 220

c) 120

d) 10

e) 66

Response: See section 4.2 Structure of Probability

Difficulty: Medium

Learning Objective: 4.2: 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.

36. 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

Response: See section 4.2 Structure of Probability

Difficulty: Easy

Learning Objective: 4.2: 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.

37. 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 ∩ 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

Response: See section 4.2 Structure of Probability

Difficulty: Easy

Learning Objective: 4.2: 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.

38. 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 ∪ 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

Response: See section 4.2 Structure of Probability

Difficulty: Easy

Learning Objective: 4.2: 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.

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}

Response: See section 4.2 Structure of Probability

Difficulty: Easy

Learning Objective: 4.2: 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.

40. 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)

Response: See section 4.2 Structure of Probability

Difficulty: Easy

Learning Objective: 4.2: 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.

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 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.

Response: See section 4.2 Structure of Probability

Difficulty: Hard

Learning Objective: 4.2: 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.

42. 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.

Response: See section 4.2 Structure of Probability

Difficulty: Hard

Learning Objective: 4.2: 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.

43. 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

Response: See section 4.2 Structure of Probability

Difficulty: Medium

Learning Objective: 4.2: 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.

44. 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 P(S).

a) 0.15

b) 0.35

c) 0.40

d) 0.55

e) 0.60

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Easy

Learning Objective: 4.3: Compare marginal, union, joint, and conditional probabilities by defining each one.

45. 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 among all students, 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

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Easy

Learning Objective: 4.3: Compare marginal, union, joint, and conditional probabilities by defining each one.

46. 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

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Easy

Learning Objective: 4.3: Compare marginal, union, joint, and conditional probabilities by defining each one.

47. One event is that individuals like lasagna and the other event is that individuals like soda, the union of these two events would be the probability of _____________.

a) both events occurring

b) at least one event occurring

c) neither event occurring

d) 0%

e) 100%

Ans: b

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Easy

Learning Objective: 4.3: Compare marginal, union, joint, and conditional probabilities by defining each one.

48. The probability that given one event has occurred that another event would occur would be an example of _________ probability.

a) marginal

b) union

c) joint

d) conditional

e) non-union

Ans: d

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Easy

Learning Objective: 4.3: Compare marginal, union, joint, and conditional probabilities by defining each one.

49. The probability of at least one of two events occurring would be an example of a____________ probability.

a) marginal

b) union

c) joint

d) conditional

e) non-union

Ans: b

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Easy

Learning Objective: 4.3: Compare marginal, union, joint, and conditional probabilities by defining each one.

50. If the CEO of Apple wanted to know the probability that if someone owned an Apple computer, they would also own a different brand computer, this would be an example of a __________ probability.

a) conditional

b) marginal

c) joint

d) non-joint

e) union

Ans: a

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Easy

Learning Objective: 4.3: Compare marginal, union, joint, and conditional probabilities by defining each one.

51. If the CEO of Apple wanted to know the probability that someone would own an Apple computer and spend more than 20 hours each week on the internet would be an example of a _____________ probability.

a) unconditional

b) union

c) joint

d) marginal

e) conditional

Ans: c

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Easy

Learning Objective: 4.3: Compare marginal, union, joint, and conditional probabilities by defining each one.

52. The CEO of Apple wanted to know the probability that someone would own an Apple computer or spend more than 20 hours each week on the internet, this would be an example of a ______________ probability.

a) union

b) unconditional

c) marginal

d) conditional

e) joint

Ans: a

Response: See section 4.3 Marginal, Union, Joint, and Conditional Probabilities

Difficulty: Easy

Learning Objective: 4.3: Compare marginal, union, joint, and conditional probabilities by defining each one.

53. 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

Response: See section 4.4 Addition Laws

Difficulty: Medium

Learning Objective: 4.4: 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.

54. 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) 0.07

b) 0.10

c) 0.20

d) 0.23

e) 0.37

Response: See section 4.4 Addition Laws

Difficulty: Medium

Learning Objective: 4.4: 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.

55. Max Sandlin researched 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) 0.10

Response: See section 4.4 Additional Laws

Difficulty: Medium

Learning Objective: 4.4: 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.

56. Given P(A) = 0.40, P(B) = 0.50, P(A ∩ B) = 0.15. Find P(A ∪ B).

a) 0.90

b) 1.05

c) 0.75

d) 0.65

e) 0.60

Response: See section 4.4 Additional Laws

Difficulty: Easy

Learning Objective: 4.4: 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.

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 (Male) = ________

a) 0.48

b) 0.50

c) 0.20

d) 0.02

e) 0.60

Response: See section 4.4 Addition Laws

Difficulty: Medium

Learning Objective: 4.4: 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.

58. 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

Response: See section 4.4 Addition Laws

Difficulty: Medium

Learning Objective: 4.4: 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.

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 (SUV) = ___________.

a) 0.30

b) 0.40

c) 0.12

d) 0.10

e) 0.60

Response: See section 4.4 Addition Laws

Difficulty: Medium

Learning Objective: 4.4: 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.

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

Response: See section 4.4 Addition Laws

Difficulty: Medium

Learning Objective: 4.4: 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.

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 (Healthcare ∪ Electronics) = _______.

a) 0.25

b) 0.85

c) 0.60

d) 0.75

e) 0.90

Response: See section 4.4 Addition laws

Difficulty: Medium

Learning Objective: 4.4: 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.

62. The table below provides summary information about the 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

Response: See section 4.4 Addition Laws

Difficulty: Easy

Learning Objective: 4.4: 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.

63. The table below provides summary information about the 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 is also under 20 years old?

a) 0.08

b) 0.18

c) 0.52

d) 0.26

e) 0.78

Response: See Section 4.4 Addition Laws

Difficulty: Easy

Learning Objective: 4.4: 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.

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 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

Response: See section 4.4 Addition Laws

Difficulty: Easy

Learning Objective: 4.4: 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.

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, 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

Response: See section 4.4 Addition Laws

Difficulty: Easy

Learning Objective: 4.4: 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.

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 either overweight or exercises regularly or both?

a) 0.40

b) 0.38

c) 0.20

d) 0.42

e) 0.10

Response: See section 4.4 Addition laws

Difficulty: Medium

Learning Objective: 4.4: 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

67. 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 ∩ SUV) = _______.

a) 0.30

b) 0.40

c) 0.12

d) 0.10

e) 0.60

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

68. 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

Response: See section 4.5 Multiplication Laws

Difficulty: Hard

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

69. Suppose that 3% of all TVs made by a company in 2018 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

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

70. A recent survey found that 24% of people in Michigan like oatmeal. If the probability that someone lives in Michigan is 4.8%, what is the probability that someone lives in Michigan and likes oatmeal?

a) 28.4%

b) 24.0%

c) 4.8%

d) 19.2%

e) 1.2%

Ans: e

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

71. A recent survey found that 24% of people in Michigan like oatmeal. If the probability that someone lives in Michigan is 4.8%. What is the probability that you choose two people in the US and they are both from Michigan?

a) 28.4%

b) 24.0%

c) 0.2%

d) 100.0%

e) 48.0%

Ans: c

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

72. A recent survey found that 24% of people in Michigan like oatmeal. If the probability that someone lives in Michigan is 4.8%. What is the probability that two people from Michigan would both like oatmeal?

a) 5.8%

b) 24.0%

c) 4.8%

d) 48.0%

e) 1.2%

Ans: a

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

a) 63%

b) 22%

c) 29%

d) 51%

e) 32%

Ans: b

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

74. Given the following joint probability table, find the probability that a dog is small and takes less than 30-minute walks?

a) 63%

b) 22%

c) 29%

d) 51%

e) 32%

Ans: c

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

Learning Objective: 4.5 Calculate joint probabilities of both independent and dependent events using the general and special laws of multiplication.

75. 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

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent

76. 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

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent.

77. 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

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent

78. 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

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent

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

a) 0.45

b) 0.135

c) 0.30

d) 0.111

e) 0.167

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent

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

a) 0.45

b) 0.135

c) 0.30

d) 0.111

e) 0.167

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent

81. Given P (A) = 0.45, P (B) = 0.30, P (A ∩ 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

Response: See section 4.6 Conditional Probability

Difficulty: Hard

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent

82. 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

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent.

83. The table below provides summary information about the 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

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent.

84. 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

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent

85. 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

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent.

86. 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

Response: See section 4.6 Conditional Probability

Difficulty: Medium

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent.

87. 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) ≠ P (B)

b) Yes, because P (B) = P(C)

c) No, because P (25 or older | B) ≠ P (25 or older)

d) Yes, because P (25 or older ∩ B) ≠ 0

e) No, because age and package design are different things

Response: See section 4.6 Conditional Probability

Difficulty: Hard

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent.

88. 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 ∩ D’) = ___________.

a) 0.20

b) 0.63

c) 0.90

d) 0.18

e) 0.78

Response: See section 4.6 Revision of Probabilities: Bayes’ Rule

Difficulty: Hard

Learning Objective: 4.6: Calculate conditional probabilities using Bayes’ rule.

89. 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

Response: See section 4.6 Revision of Probabilities: Bayes’ Rule

Difficulty: Hard

Learning Objective: 4.6: Calculate conditional probabilities using Bayes’ rule.

90. 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

Response: See section 4.7 Revision of Probabilities: Bayes’ Rule

Difficulty: Medium

Learning Objective: 4.7: Calculate conditional probabilities using Bayes’ rule.

91. 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

Response: See section 4.7 Revision of Probabilities: Bayes’ Rule

Difficulty: Hard

Learning Objective: 4.7: Calculate conditional probabilities using Bayes’ rule.

92. 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

Response: See section 4.7 Revision of Probabilities: Bayes’ Rule

Difficulty: Hard

Learning Objective: 4.7: Calculate conditional probabilities using Bayes’ rule.

93. 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

Response: See section 4.7 Revision of Probabilities: Bayes’ Rule

Difficulty: Hard

Learning Objective: 4.7: Calculate conditional probabilities using Bayes’ rule.

94. 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

Response: See section 4.7 Revision of Probabilities: Bayes’ Rule

Difficulty: Hard

Learning Objective: 4.7: Calculate conditional probabilities using Bayes’ rule.

95. 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

Response: See section 4.1 Introduction to Probability

Difficulty: Easy

AACSB: Reflective thinking

Bloom’s level: Application

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

96. 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

Response: See section 4.1 Introduction to Probability

Difficulty: Hard

AACSB: Analytic

Bloom’s level: Application

Learning Objective: 4.1: Describe what probability is and how to differentiate among the three methods of assigning probabilities.

97. 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

Response: See section 4.2 Structure of Probability

Difficulty: Medium

AACSB: Reflective thinking

Bloom’s level: Application

Learning Objective: 4.2: 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.

98. 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

Response: See section 4.2 Structure of Probability

Difficulty: Medium

AACSB: Reflective thinking

Bloom’s level: Application

Learning Objective: 4.2: 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.

99. 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

Response: See section 4.2 Structure of Probability

Difficulty: Medium

AACSB: Reflective thinking

Bloom’s level: Application

Learning Objective: 4.2: 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.

100. 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 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

Response: See section 4.3 Marginal, Joint, Union, and Conditional Probabilities

Difficulty: Medium

AACSB: Reflective thinking

Bloom’s level: Application

Learning Objective: 4.3: Compare marginal, union, joint, and conditional probabilities by defining each one.

101. 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 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%

Response: See section 4.4 Addition Laws

Difficulty: Medium

AACSB: Analytic

Bloom’s level: Application

Learning Objective: 4.4: 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.

102. 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

Response: See section 4.4 Addition Laws

Difficulty: Hard

AACSB: Reflective thinking

Bloom’s level: Application

Learning Objective: 4.4: 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.

103. 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) 0.131

b) 0.128

c) 0.126

d) 0.124

e) 0.122

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

AACSB: Reflective thinking

Bloom’s level: Application

Learning Objective: 4.5: Calculate joint probabilities of both independent and dependent variables using the general and special laws of multiplication.

104. 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

Response: See section 4.5 Multiplication Laws

Difficulty: Medium

AACSB: Reflective thinking

Bloom’s level: Application

Learning Objective: 4.5: Calculate joint probabilities of both independent and dependent variables using the general and special laws of multiplication.

105. 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 labeled 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) 0.13

c) 0.66

d) 0.60

e) 0.58

Response: See section 4.6 Conditional Probability

Difficulty: Medium

AACSB: Reflective thinking

Bloom’s level: Application

Learning Objective: 4.6: Calculate conditional probabilities with various forms of the law of conditional probability, and use them to determine if two events are independent.

106. There are three companies that produce a critical electronic navigation component (ENC) used in the aerospace industry. These companies are Alice Manufacturing, Byte International, and Cognizant Technologies. Alice makes 85% of the ENCs, Byte makes 10%, and Cognizant makes the remaining 5%. The ENCs made by Alice have a 2.5% rate of defects, the ones made by Byte have a 4.0% rate of defects, and the ones made by Cognizant have a 6% rate of defects. If an ENC is randomly selected from the general population of ENCs, the probability that it was made by Alice is _______. If this ENC is later tested and found to be defective, the probability that it was made by Alice is _______.

a) 0.15; 0.85

b) 0.85; 0.85

c) 0.85; 0.77

d) 0.85; 0.76

e) 0.85; 0.75

Response: See section 4.7 Revision of Probabilities: Bayes’ Rule

Difficulty: Hard

AACSB: Analytic

Bloom’s level: Application

Learning Objective: 4.7: Calculate conditional probabilities using Bayes’ rule.