Chapter 2 – Introduction to Probability
True / False
1. Two events that are independent cannot be mutually exclusive.
a. True
b. False
2. A joint probability can have a value greater than 1.
a. True
b. False
3. The intersection of A and Ac is the entire sample space.
a. True
b. False
4. If 50 of 250 people contacted make a donation to the city symphony, then the relative frequency method assigns a
probability of .2 to the outcome of making a donation.
a. True
b. False
5. An automobile dealership is waiting to take delivery of nine new cars. Today, anywhere from zero to all nine cars
might be delivered. It is appropriate to use the classical method to assign a probability of 1/10 to each of the possible
numbers that could be delivered.
a. True
b. False
6. When assigning subjective probabilities, use experience, intuition, and any available data.
a. True
b. False
7. P(A B) ≥ P(A)
Chapter 2 – Introduction to Probability
a. True
b. False
8. If P(A|B) = .4 and P(B) = .6, then P(A B) = .667.
a. True
b. False
9. Bayes’ theorem provides a way to transform prior probabilities into posterior probabilities.
a. True
b. False
ANSWER: True
POINTS: 1
TOPICS: Bayes’ Theorem
10. If P(A B) = P(A) + P(B), then A and B are mutually exclusive.
a. True
11. If A and B are mutually exclusive events, then P(A | B) = 0.
a. True
b. False
12. If A and B are independent events with P(A) = 0.1 and P(B) = 0.5, then P(A B) = .6.
a. True
b. False
13. A graphical device used for enumerating sample points in a multiple-step experiment is a Venn diagram.
a. True
b. False
Chapter 2 – Introduction to Probability
14. A posterior probability is a conditional probability.
a. True
b. False
15. If A and B are independent events, then P(A B) = P(A)P(B).
a. True
b. False
16. Two events that are mutually exclusive cannot be independent.
a. True
b. False
17. P(A|B) = P(B|A) for all events A and B.
a. True
b. False
18. P(A|B) = 1 − P(B|A) for all events A and B.
a. True
b. False
19. P(A|B) = P(AC|B) for all events A and B.
a. True
b. False
20. P(A|B) + P(A|BC) = 1 for all events A and B.
a. True
b. False
Chapter 2 – Introduction to Probability
21. Which of the following is not a valid representation of a probability?
a. 35%
b. 0
c. 1.04
d. 3/8
22. A list of all possible outcomes of an experiment is called
a. the sample space.
b. the sample point.
c. the experimental outcome.
d. the likelihood set.
23. Which of the following is not a proper sample space when all undergraduates at a university are considered?
a. S = {in-state, out-of-state}
b. S = {freshmen, sophomores}
c. S = {age under 21, age 21 or over}
d. S = {a major within business, no business major}
24. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event
B mean the account is that of a new customer. The complement of A is
a. all new customers.
b. all accounts fewer than 31 or more than 60 days past due.
c. all accounts from new customers and all accounts that are from 31 to 60 days past due.
d. all new customers whose accounts are between 31 and 60 days past due.
25. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event
B mean the account is that of a new customer. The union of A and B is
a. all new customers.
b. all accounts fewer than 31 or more than 60 days past due.
c. all accounts from new customers and all accounts that are from 31 to 60 days past due.
d. all new customers whose accounts are between 31 and 60 days past due.
Chapter 2 – Introduction to Probability
26. In the set of all past due accounts, let the event A mean the account is between 31 and 60 days past due and the event
B mean the account is that of a new customer. The intersection of A and B is
a. all new customers.
b. all accounts fewer than 31 or more than 60 days past due.
c. all accounts from new customers and all accounts that are from 31 to 60 days past due.
d. all new customers whose accounts are between 31 and 60 days past due.
27. The probability of an event
a. is the sum of the probabilities of the sample points in the event.
b. is the product of the probabilities of the sample points in the event.
c. is the maximum of the probabilities of the sample points in the event.
d. is the minimum of the probabilities of the sample points in the event.
28. If P(A B) = 0
a. A and B are independent events.
b. P(A) + P(B) = 1
c. A and B are mutually exclusive events.
d. either P(A) = 0 or P(B) = 0.
29. If P(A|B) = .4, then
a. P(B|A) = .6
b. P(A)*P(B) = .4
c. P(A) / P(B) = .4
d. None of the alternatives is correct.
30. If P(A|B) = .2 and P(Bc) = .6, then P(B|A)
a. is .8
b. is .12
c. is .33
d. cannot be determined.
31. A method of assigning probabilities that assumes the experimental outcomes are equally likely is referred to as the
Chapter 2 – Introduction to Probability
a. objective method
b. classical method
c. subjective method
d. experimental method
32. When the results of experimentation or historical data are used to assign probability values, the method used to assign
probabilities is referred to as the
a. relative frequency method
b. subjective method
c. classical method
d. posterior method
33. A method of assigning probabilities based upon judgment is referred to as the
a. relative method
b. probability method
c. classical method
d. None of the alternatives is correct.
34. The union of events A and B is the event containing
a. all the sample points common to both A and B
b. all the sample points belonging to A or B
c. all the sample points belonging to A or B or both
d. all the sample points belonging to A or B, but not both
35. If P(A) = 0.38, P(B) = 0.83, and P(A B) = 0.27; then P(A B) =
a. 1.21
b. 0.94
c. 0.72
d. 1.48
36. When the conclusions based upon the aggregated crosstabulation can be completely reversed if we look at the
unaggregated data, the occurrence is known as
a. reverse correlation
b. inferential statistics
Chapter 2 – Introduction to Probability
c. Simpson’s paradox
d. disaggregation
37. Before drawing any conclusions about the relationship between two variables shown in a crosstabulation, you should
a. investigate whether any hidden variables could affect the conclusions
b. construct a scatter diagram and find the trendline
c. develop a relative frequency distribution
d. construct an ogive for each of the variables
38. Revised probabilities of events based on additional information are
a. joint probabilities
b. posterior probabilities
c. marginal probabilities
d. complementary probabilities
39. The probability of an intersection of two events is computed using the
a. addition law
b. subtraction law
c. multiplication law
d. division law
40. Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical method for
computing probability is used, the probability that the next customer will purchase a computer is
a. 0.25
b. 0.50
c. 0.75
d. 1.00
41. The probability of at least one head in two flips of a coin is
a. 0.33
b. 0.50
c. 0.75
d. 1.00
Chapter 2 – Introduction to Probability
42. Posterior probabilities are computed using
a. the classical method
b. Chebyshev’s theorem
c. the empirical rule
d. Bayes’ theorem
43. The complement of P(A | B) is
a. P(AC | B)
b. P(A | BC)
c. P(B | A)
d. P(A B)
44. An element of the sample space is
a. an event
b. an estimator
c. a sample point
d. an outlier
45. Posterior probabilities are
a. simple probabilities
b. marginal probabilities
c. joint probabilities
d. conditional probabilities
46. The range of probability is
a. any value larger than zero
b. any value between minus infinity to plus infinity
c. zero to one
d. any value between –1 to 1
47. Any process that generates well-defined outcomes is
a. an event
b. an experiment
c. a sample point
d. None of the other answers is correct.
Chapter 2 – Introduction to Probability
48. An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is
a. 16
b. 8
c. 4
d. 2
49. Three applications for admission to a local university are checked to determine whether each applicant is male or
female. The number of sample points in this experiment is
a. 2
b. 4
c. 6
d. 8
50. A graphical device used for enumerating sample points in a multiple-step experiment is a
a. bar chart
b. pie chart
c. histogram
d. None of the other answers is correct.
51. An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and P(E3) = 0.4. The probability of outcome
E4 is
a. 0.500
b. 0.024
c. 0.100
d. 0.900
52. A(n) __________ is a graphical representation in which the sample space is represented by a rectangle and events are
represented as circles.
a. frequency polygon
b. histogram
c. Venn diagram
d. tree diagram
53. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∩ B) =
a. 0.30
b. 0.15
Chapter 2 – Introduction to Probability
c. 0.00
d. 0.20
54. Which of the following statements is(are) always true?
a. -1 ≤ P(Ei) ≤ 1
b. P(A) = 1 − P(Ac)
c. P(A) + P(B) = 1
d. both P(A) = 1 − P(Ac) and P(A) + P(B) = 1
55. One of the basic requirements of probability is
a. for each experimental outcome Ei, we must have P(Ei) ≥ 1
b. P(A) = P(Ac) − 1
c. if there are k experimental outcomes, then P(E1) + P(E2) + … + P(Ek) = 1
d. both P(A) = P(Ac) − 1 and if there are k experimental outcomes, then P(E1) + P(E2) + … + P(Ek) = 1
56. Events A and B are mutually exclusive. Which of the following statements is also true?
a. A and B are also independent
b. P(A B) = P(A)P(B)
c. P(A B) = P(A) + P(B)
d. P(A ∩ B) = P(A) + P(B)
Subjective Short Answer
57. A market study taken at a local sporting goods store showed that of 20 people questioned, 6 owned tents, 10 owned
sleeping bags, 8 owned camping stoves, 4 owned both tents and camping stoves, and 4 owned both sleeping bags and
camping stoves.
Let: Event A = owns a tent
Event B = owns a sleeping bag
Event C = owns a camping stove
and let the sample space be the 20 people questioned.
a. Find P(A), P(B), P(C), P(A C), P(B C).
b. Are the events A and C mutually exclusive? Explain briefly.
c. Are the events B and C independent events? Explain briefly.
d. If a person questioned owns a tent, what is the probability he also owns a camping stove?
e. If two people questioned own a tent, a sleeping bag, and a camping stove, how many own only a camping stove? In
this case is it possible for 3 people to own both a tent and a sleeping bag, but not a camping stove?
Chapter 2 – Introduction to Probability
58. An accounting firm has noticed that of the companies it audits, 85% show no inventory shortages, 10% show small
inventory shortages and 5% show large inventory shortages. The firm has devised a new accounting test for which it
believes the following probabilities hold:
P(company will pass test | no shortage) = .90
P(company will pass test | small shortage) = .50
P(company will pass test | large shortage) = .20
a. If a company being audited fails this test, what is the probability of a large or small inventory shortage?
b. If a company being audited passes this test, what is the probability of no inventory shortage?
59. An investment advisor recommends the purchase of stock shares in Infomatics, Inc. He has made the following
predictions:
P(Stock goes up 20% | Rise in GDP) = .6
P(Stock goes up 20% | Level GDP) = .5
P(Stock goes up 20% | Fall in GDP) = .4
An economist has predicted that the probability of a rise in the GDP is 30%, whereas the probability of a fall in the GDP
is 40%.
a. What is the probability that the stock will go up 20%?
b. We have been informed that the stock has gone up 20%. What is the probability of a rise or fall in the GDP?
60. Global Airlines operates two types of jet planes: jumbo and ordinary. On jumbo jets, 25% of the passengers are on
business while on ordinary jets 30% of the passengers are on business. Of Global’s air fleet, 40% of its capacity is
provided on jumbo jets. (Hint: The 25% and 30% values are conditional probabilities stated as percentages.)
a. What is the probability a randomly chosen business customer flying with Global is on a jumbo jet?
b. What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?