CHAPTER 4

PROBABILITY

CHAPTER LEARNING OBJECTIVES

1. Describe what probability is and when one would use it, and how to differentiate among three methods of assigning probabilities. The study of probability addresses ways of assigning probabilities, types of probabilities, and laws of probabilities. Probabilities support the notion of inferential statistics. Using sample data to estimate and test hypotheses about population parameters is done with uncertainty. If samples are taken at random, probabilities can be assigned to outcomes of the inferential process. Three methods of assigning probabilities are (a) the classical method, (b) the relative frequency of occurrence method, and (c) subjective probabilities. The classical method can assign probabilities a priori, or before the experiment takes place. It relies on the laws and rules of probability. The relative frequency of occurrence method assigns probabilities based on historical data or empirically derived data. Subjective probabilities are based on the feelings, knowledge, and experience of the person determining the probability.

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. Certain special types of events necessitate amendments to some of the laws of probability: mutually exclusive events and independent events. Mutually exclusive events are events that cannot occur at the same time, so the probability of their intersection is zero. In determining the union of two mutually exclusive events, the law of addition is amended by the deletion of the intersection. With independent events, the occurrence of one has no impact or influence on the occurrence of the other. Certain experiments, such as those involving coins or dice, naturally produce independent events. Other experiments produce independent events when the experiment is conducted with replacement. If events are independent, the joint probability is computed by multiplying the individual probabilities, which is a special case of the law of multiplication. Three techniques for counting the possibilities in an experiment are the mn counting rule, the Nⁿ possibilities, and combinations. The mn counting rule is used to determine in how many total possible ways an experiment can occur in a series of sequential operations. The Nⁿ formula is applied when sampling is being done with replacement or events are independent. Combinations are used to determine the possibilities when sampling is being done without replacement.

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

Four types of probability are marginal probability, conditional probability, joint probability, and union probability.

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. The general law of addition is used to compute the probability of a union. The general law of multiplication is used to compute joint probabilities. The conditional law is used to compute conditional probabilities.

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

6. Calculate conditional probabilities with various forms of the law of conditional probability and use them to determine if two events are independent. The general law of addition is used when we need to find the probability of the union of two events (X or Y or both occurring). The general law of multiplication is used to find the probability of two events X and Y happening together (joint probability). Conditional probabilities are used when we want to incorporate prior knowledge one may have regarding the two events studied.

7. Calculate conditional probabilities using Bayes’ rule. Bayes’ rule is a method that can be used to revise probabilities when new information becomes available; it is a variation of the conditional law. Bayes’ rule takes prior probabilities of events occurring and adjusts or revises those probabilities on the basis of information about what subsequently occurs.

TRUE-FALSE STATEMENTS

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.

Difficulty: Easy

Learning Objective: Describe what probability is, when one would use it, and how to differentiate among three methods of assigning probabilities

Section Reference: 4.1 Introduction to Probability

Blooms: Knowledge

AACSB: Analytic

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

Difficulty: Easy

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

Section Reference: 4.1 Introduction to Probability

Blooms: Knowledge

AACSB: Analytic

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

Difficulty: Easy

Learning Objective:

Learning Objective: Describe what probability is, when one would use it, and how to differentiate among three methods of assigning probabilities

Section Reference: 4.1 Introduction to Probability

Blooms: Knowledge

AACSB: Analytic

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 relative frequency of occurrence method.

Difficulty: Easy

Learning Objective: Describe what probability is, when one would use it, and how to differentiate among three methods of assigning probabilities

Section Reference: 4.1 Introduction to Probability

Blooms: Knowledge

AACSB: Analytic

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

Difficulty: Easy

Learning Objective: Describe what probability is, when one would use it, and how to differentiate among three methods of assigning probabilities

Section Reference: 4.1 Introduction to Probability

Blooms: Knowledge

AACSB: Analytic

6. A probability of an event will have a value ranging from -1 to +1.

Difficulty: Easy

Learning Objective: Describe what probability is, when one would use it, and how to differentiate among three methods of assigning probabilities

Section Reference: 4.1 Introduction to Probability

Blooms: Knowledge

AACSB: Analytic

7. An experiment is a process that produces outcomes.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

8. An event is a process that produces outcomes.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

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

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

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

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

11. The objective of statistics is to make inferences about a population based on information contained in a sample.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

12. The probability of an event A is equal to the sum of the probabilities of the sample points in A.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

13. The symbol ∪ represents the union of two events.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

14. The symbol ∪ represents the intersection of two events.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

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

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

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

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

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

Difficulty: Hard

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

18. All possible elementary events for an experiment is referred to as collectively exhaustive events.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

19. The mn counting rule may only be used when there are two operations from which to count.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

20. Sampling n items from a population of size N without replacements is referred to as combinations.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

21. Events A and B are said to be independent if either P(A⎢B) = P(B) or if P(B⎢A) = P(A).

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

22. Buyers of television sets are offered a choice of one of three different styles. There are 9 different outcomes if two customers make a selection.

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Application

AACSB: Analytic

23. Buyers of television sets are offered a choice of one of three different styles. There are 720 different outcomes if ten customers make a selection.

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Application

AACSB: Analytic

24. There are 4 simple events in a two-coin toss experiment.

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

25. 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.

Blooms: Knowledge

AACSB: Analytic

26. 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.

Blooms: Knowledge

AACSB: Analytic

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

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.

Blooms: Knowledge

AACSB: Analytic

28. A joint probability is the probability that at least one of two events occur.

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.

Blooms: Knowledge

AACSB: Analytic

29. A joint probability is the same as the intersection of two or more events.

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.

Blooms: Knowledge

AACSB: Analytic

30. In the conditional probability P(E₁|E₂) is interpreted as given that E₂ has occurred what is the probability of E₁ occurring.

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.

Blooms: Knowledge

AACSB: Analytic

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

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.4 Addition Laws

Blooms: Application

AACSB: Analytic

32. The general law of addition is P(X∪Y) = P(X) + P(Y) – P(X∩Y).

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.4 Addition Laws

Blooms: Application

AACSB: Analytic

33. The general law of addition is P(X∩Y) = P(X) + P(Y) – P(X∪Y).

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.4 Addition Laws

Blooms: Application

AACSB: Analytic

34. 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.

Blooms: Application

AACSB: Analytic

35. 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.

Blooms: Application

AACSB: Analytic

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

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.

Blooms: Application

AACSB: Analytic

37. 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%.

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.

Blooms: Application

AACSB: Analytic

38. 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.

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.

Blooms: Application

AACSB: Analytic

39. If P(X|Y) = P(X) then the events X and Y 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.

Blooms: Application

AACSB: Analytic

40. 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.

Difficulty: Medium

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

Section Reference: 4.6 Conditional Probability

Blooms: Application

AACSB: Analytic

41. 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.

Difficulty: Medium

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

Section Reference: 4.6 Conditional Probability

Blooms: Knowledge

AACSB: Analytic

42. 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.

Difficulty: Medium

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

Section Reference: 4.6 Conditional Probability

Blooms: Knowledge

AACSB: Analytic

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

Difficulty: Easy

Learning Objective: Calculate conditional probabilities using Bayes’ rule.

Section Reference: 4.7 Revision of Probabilities: Bayes’ Rule

Blooms: Knowledge

AACSB: Analytic

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

Difficulty: Easy

Learning Objective: Calculate conditional probabilities using Bayes’ rule.

Section Reference: 4.7 Revision of Probabilities: Bayes’ Rule

Blooms: Knowledge

AACSB: Analytic

45. P(B⏐A) denotes the posterior probability of event B given event A.

Difficulty: Easy

Learning Objective: Calculate conditional probabilities using Bayes’ rule.

Section Reference: 4.7 Revision of Probabilities: Bayes’ Rule

Blooms: Knowledge

AACSB: Analytic

46. P(B⏐A) denotes a conditional probability.

Difficulty: Easy

Learning Objective: Calculate conditional probabilities using Bayes’ rule.

Section Reference: 4.7 Revision of Probabilities: Bayes’ Rule

Blooms: Knowledge

AACSB: Analytic

47. P(B) denotes an unconditional probability.

Difficulty: Easy

Learning Objective: Calculate conditional probabilities using Bayes’ rule.

Section Reference: 4.7 Revision of Probabilities: Bayes’ Rule

Blooms: Knowledge

AACSB: Analytic

MULTIPLE CHOICE QUESTIONS

48. 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, when one would use it, and how to differentiate among three methods of assigning probabilities

Blooms: Knowledge

AACSB: Analytic

49. 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

Difficulty: Medium

Describe what probability is, when one would use it, and how to differentiate among three methods of assigning probabilities

Section Reference: 4.1 Introduction to Probability

Blooms: Knowledge

AACSB: Analytic

50. Which of the following is not a legitimate probability value?

a) 0.67

b) 15/16

c) 0.23

d) 4/3

e) 0.98

Difficulty: Easy

Describe what probability is, when one would use it, and how to differentiate among three methods of assigning probabilities

Section Reference: 4.1 Introduction to Probability

Blooms: Knowledge

AACSB: Analytic

51. 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, when one would use it, and how to differentiate among three methods of assigning probabilities

Blooms: Knowledge

AACSB: Analytic

52. 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) prior probability

e) posterior probability

Response: See section 4.1 Introduction to Probability

Difficulty: Medium

Learning Objective: 4.1: Describe what probability is, when one would use it, and how to differentiate among three methods of assigning probabilities

Blooms: Knowledge

AACSB: Analytic

53. 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

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

54. The union of two events, M and N is denoted by ___.

a) (MN)

b) M ⊂ N

c) M ∩ N

d) M ∪ N

e) M ⊃ N

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

55. The intersection of two events, M and N is denoted by ___.

a) (MN)

b) M ⊂ N

c) M ∩ N

d) M ∪ N

e) M ⊃ N

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

56. In a set of 15 aluminum castings, two castings are defective (D), and the remaining thirteen are good (G). A quality control inspector randomly selects three of the fifteen castings without replacement and classifies each as defective (D) or good (G). How large is the sample space?

a) 3,375

b) 2,730

c) 455

d) 15

e) 3

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Application

AACSB: Analytic

57. In a set of 10 aluminum castings, two castings are defective (D), and the remaining eight are good (G). A quality control inspector randomly selects three of the ten castings with replacement and classifies each as defective (D) or good (G). How large is the sample space?

a) 1,000

b) 720

c) 100

d) 10

e) 3

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Application

AACSB: Analytic

58. Five people are selected from a group of 20 to form a committee. How many different committee combinations could be formed?

a) 100

b) 120

c) 15,504

d) 3.2 Million

e) 9,5 Billion

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Application

AACSB: Analytic

59. Buyers of television sets are offered a choice of one of three different styles. How many different outcomes could result if two customers make a selection?

a) 3

b) 5

c) 6

d) 8

e) 9

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Application

AACSB: Analytic

60. Buyers of television sets are offered a choice of one of three different styles. How many different outcomes could result if ten customers make a selection?

a) 30

b) 120

c) 720

d) 1000

e) 59049

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Application

AACSB: Analytic

61. 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

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

62. Consider the following sample space, S, and several events defined in 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

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Application

AACSB: Analytic

63. Consider the following sample space, S, and several events defined in 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

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Application

AACSB: Analytic

64. 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}

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Application

AACSB: Analytic

65. If X and Y are mutually exclusive, then ___.

a) the probability of the union is zero

b) P(X) = 1 - P(Y)

c) the probability of the intersection is zero

d) the probability of the union is one

e) P(Y) = P(X)

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.2 Structure of Probability

Blooms: Knowledge

AACSB: Analytic

66. 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.

Blooms: Analysis

AACSB: Analytic

67. 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.

Blooms: Analysis

AACSB: Analytic

68. 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.

Blooms: Application

AACSB: Analytic

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

a) 0.15

b) 0.30

c) 0.40

d) 0.55

e) 0.60

Difficulty: Medium

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

Section Reference: 4.3 Marginal, Union, Joint, and Conditional Probabilities

Blooms: Application

AACSB: Analytic

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

a) 0.15

b) 0.70

c) 0.55

d) 0.12

e) 0.60

Difficulty: Medium

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

Section Reference: 4.3 Marginal, Union, Joint, and Conditional Probabilities

Blooms: Application

AACSB: Analytic

71. 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%

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.

Blooms: Knowledge

AACSB: Analytic

72. 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

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.

Blooms: Knowledge

AACSB: Analytic

73. 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

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.

Blooms: Knowledge

AACSB: Analytic

74. 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

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.

Blooms: Knowledge

AACSB: Analytic

75. 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

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.

Blooms: Knowledge

AACSB: Analytic

76. 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

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.

Blooms: Knowledge

AACSB: Analytic

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

a) 0.15

b) 0.75

c) 0.375

d) 0.50

e) 0.80

Difficulty: Hard

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

Section Reference: 4.3 Marginal, Union, Joint, and Conditional Probabilities

Blooms: Knowledge

AACSB: Analytic

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

a) 0.15

b) 0.85

c) 0.70

d) 0.55

e) 0.90

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.4 Addition Laws

Blooms: Application

AACSB: Analytic

79. Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Plano Power Plant. 10% 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

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.4 Addition Laws

Blooms: Application

AACSB: Analytic

80. Max Sandlin is exploring the characteristics of stock market investors. He found that 60% 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

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.4 Addition Laws

Blooms: Application

AACSB: Analytic

81. 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

Difficulty: Easy

Learning Objective: 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.

Section Reference: 4.4 Addition Laws

Blooms: Application

AACSB: Analytic

82. 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 what is 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.

Blooms: Application

AACSB: Analytic

83. 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 what is 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.

Blooms: Application

AACSB: Analytic

84. 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 what is 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.

Blooms: Application

AACSB: Analytic

85. The table below provides summary information about students in a class. The gender of each individual and the major is given.

A student is randomly selected from this group, and it is found that the student is majoring in finance. What is the probability that the student is a male?

a) 0.21

b) 0.10

c) 0.56

d) 0.48

e) 0.78

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.

Section Reference: 4.4 Addition Laws

Blooms: Application

AACSB: Analytic

86. 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

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.

Section Reference: 4.4 Addition Laws

Blooms: Application

AACSB: Analytic

87. 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 what is 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.

Blooms: Application

AACSB: Analytic

88. 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 what is 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.

Blooms: Application

AACSB: Analytic

89. The table below provides summary information about the students in a class. The gender 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.

Blooms: Application

AACSB: Analytic

90. The table below provides summary information about the students in a class. The gender 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.

Blooms: Application

AACSB: Analytic

91. 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.

Blooms: Application

AACSB: Analytic

92. 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.

Blooms: Application

AACSB: Analytic

93. 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

Blooms: Application

AACSB: Analytic

94. 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

Difficulty: Medium

Learning Objective: 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.

Section Reference: 4.4 Addition Laws

Blooms: Knowledge

AACSB: Analytic

95. A recent survey of Financial Post (FP) readers reported that 40% of their subscribers regularly read the Wall Street Journal (WSJ), 32% read Time (T), and 11% read both the WSJ and T. What is the probability that a randomly selected reader reads WSJ or T or both?

a) 0.09

b) 0.11

c) 0.61

d) 0.72

e) 0.87

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

Blooms: Application

AACSB: Analytic

96. 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.

Blooms: Application

AACSB: Analytic

97. 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.

Blooms: Application

AACSB: Analytic

98. 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.

Blooms: Application

AACSB: Analytic

99. 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%

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.

Blooms: Application

AACSB: Analytic

100. 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%

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.

Blooms: Application

AACSB: Analytic

101. 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%

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.

Blooms: Application

AACSB: Analytic

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

a) 63%

b) 22%

c) 29%

d) 51%

e) 32%

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.

Blooms: Application

AACSB: Analytic

103. 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%

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.

Blooms: Application

AACSB: Analytic

104. 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

Blooms: Application

AACSB: Analytic

105. 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

Difficulty: Medium

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

Section Reference: 4.6 Conditional Probability

Blooms: Application

AACSB: Analytic

106. 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

Difficulty: Medium

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

Section Reference: 4.6 Conditional Probability

Blooms: Application

AACSB: Analytic

107. 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

Difficulty: Medium

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

Section Reference: 4.6 Conditional Probability

Blooms: Application

AACSB: Analytic

108. Given P (A) = 0.40, P (B) = 0.50, P (A ∩ B) = 0.15. Find P (A|B).

a) 0.20

b) 0.80

c) 0.30

d) 0.375

e) 0.15

Difficulty: Medium

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

Section Reference: 4.6 Conditional Probability

Blooms: Application

AACSB: Analytic

109. Given P (A) = 0.40, P (B) = 0.50, P (A ∩ B) = 0.15. Find P (B|A).

a) 0.20

b) 0.80

c) 0.30

d) 0.375

e) 0.15

Difficulty: Medium

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

Section Reference: 4.6 Conditional Probability

Blooms: Application

AACSB: Analytic

110. Given P (A) = 0.40, P (B) = 0.50, P (A ∩ B) = 0.15. Which of the following is true?

a) A and B are independent.

b) A and B are mutually exclusive.

c) A and B are collectively exhaustive.

d) A and B are not independent.

e) A and B are complimentary.

Difficulty: Medium

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

Section Reference: 4.6 Conditional Probability

Blooms: Application

AACSB: Analytic

111. 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

Blooms: Application

AACSB: Analytic

112. 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

Blooms: Application

AACSB: Analytic

113. 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

Blooms: Application

AACSB: Analytic

114. 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

Difficulty: Medium

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

Section Reference: 4.6 Conditional Probability

Blooms: Application

AACSB: Analytic

115. The table below provides summary information about students in a class. The gender of each individual and the major is given.

If a student is randomly selected from this group, what is the probability that the student is a female who majors in accounting?

a) 0.18

b) 0.60

c) 0.35

d) 0.40

e) 0.78

Difficulty: Easy

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

Section Reference: 4.6 Conditional Probability

Blooms: Application

AACSB: Analytic

116. 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

Difficulty: Hard

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

Section Reference: 4.6 Conditional Probability

Blooms: Application

AACSB: Analytic

117. 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

Difficulty: Hard

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

Section Reference: 4.6 Conditional Probability

Blooms: Application

AACSB: Analytic

118. A market research firm is investigating the appeal of three package designs. The table below gives information obtained through a sample of 200 consumers. The three package designs are labelled A, B, and C. The consumers are classified according to age and package design preference.

Are “B” and “25 or older” independent and why or why not?

a) No, because P (25 or over | B) ≠ 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.

Difficulty: Hard

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

Section Reference: 4.6 Conditional Probability

Blooms: Analysis

AACSB: Analytic

119. 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

Difficulty: Medium

Learning Objective: Calculate conditional probabilities using Bayes’ rule.

Section Reference: 4.7 Revision of Probabilities: Bayes’ Rule

Blooms: Analysis

AACSB: Analytic

120. 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

Difficulty: Medium

Learning Objective: Calculate conditional probabilities using Bayes’ rule.

Section Reference: 4.7 Revision of Probabilities: Bayes’ Rule

Blooms: Application

AACSB: Analytic

121. 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

Difficulty: Medium

Learning Objective: Calculate conditional probabilities using Bayes’ rule.

Section Reference: 4.7 Revision of Probabilities: Bayes’ Rule

Blooms: Application

AACSB: Analytic

122. 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

Difficulty: Hard

Learning Objective: Calculate conditional probabilities using Bayes’ rule.

Section Reference: 4.7 Revision of Probabilities: Bayes’ Rule

Blooms: Application

AACSB: Analytic

123 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

Difficulty: Hard

Learning Objective: Calculate conditional probabilities using Bayes’ rule.

Section Reference: 4.7 Revision of Probabilities: Bayes’ Rule

Blooms: Application

AACSB: Analytic

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