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CHAPTER 6 SECTION 1: PROBABILITY
MULTIPLE CHOICE
1. An approach of assigning probabilities which assumes that all outcomes of the experiment are equally
likely is referred to as the:
a. subjective approach
b. objective approach
c. classical approach
d. relative frequency approach
ANS: C
PTS: 1
REF: SECTION 6.1
2. If A and B are mutually exclusive events with P(A) = 0.70, then P(B):
a. can be any value between 0 and 1.
b. can be any value between 0 and 0.70.
c. cannot be larger than 0.30.
d. equals 0.30.
ANS: C
PTS: 1
REF: SECTION 6.1
3. If you roll a balanced die 50 times, you should expect an even number to appear:
a. on every other roll.
b. exactly 50 times out of 100 rolls.
c. 25 times on average, over the long term.
d. All of these choices are true.
ANS: D
PTS: 1
REF: SECTION 6.1
4. The collection of all possible outcomes of an experiment is called:
a. a simple event
b. a sample space
c. a sample
d. a population
ANS: B
PTS: 1
REF: SECTION 6.1
5. Which of the following is an approach to assigning probabilities?
a. Classical approach
b. Relative frequency approach
c. Subjective approach
d. All of these choices are true.
ANS: B
PTS: 1
REF: SECTION 6.1
6. A sample space of an experiment consists of the following outcomes: 1, 2, 3, 4, and 5. Which of the
following is a simple event?
a. At least 3
b. At most 2
c. 3
d. 15
ANS: C
PTS: 1
REF: SECTION 6.1
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copied, or distributed without the prior consent of the publisher.
7. Which of the following is a requirement of the probabilities assigned to outcome Oi?
a. P(Oi)  0 for each i
b. P(Oi)  1 for each i
c. 0  P(Oi)  1 for each i
d. P(Oi) = 1 for each i
ANS: C
PTS: 1
REF: SECTION 6.1
8. If an experiment consists of five outcomes with P(O1) = 0.10, P(O2) = 0.20, P(O3) = 0.30, P(O4) =
0.15, then P(O5) is
a. 0.75
b. 0.25
c. 0.50
d. Cannot be determined from the information given.
ANS: B
PTS: 1
REF: SECTION 6.1
9. Of the last 500 customers entering a supermarket, 50 have purchased a wireless phone. If the relative
frequency approach for assigning probabilities is used, the probability that the next customer will
purchase a wireless phone is
a. 0.10
b. 0.90
c. 0.50
d. None of these choices.
ANS: A
PTS: 1
REF: SECTION 6.1
10. If two events are collectively exhaustive, what is the probability that one or the other occurs?
a. 0.00
b. 0.50
c. 1.00
d. Cannot be determined from the information given.
ANS: D
PTS: 1
REF: SECTION 6.1
11. If two events are collectively exhaustive, what is the probability that both occur at the same time?
a. 0.00
b. 0.50
c. 1.00
d. Cannot be determined from the information given.
ANS: D
PTS: 1
REF: SECTION 6.1
12. If two events are mutually exclusive, what is the probability that one or the other occurs?
a. 0.00
b. 0.50
c. 1.00
d. Cannot be determined from the information given.
ANS: D
PTS: 1
REF: SECTION 6.1
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copied, or distributed without the prior consent of the publisher.
13. If two events are mutually exclusive, what is the probability that both occur at the same time?
a. 0.00
b. 0.50
c. 1.00
d. Cannot be determined from the information given.
ANS: A
PTS: 1
REF: SECTION 6.1
14. If two events are mutually exclusive and collectively exhaustive, what is the probability that both
occur?
a. 0.00
b. 0.50
c. 1.00
d. Cannot be determined from the information given.
ANS: A
PTS: 1
REF: SECTION 6.1
15. If the two events are mutually exclusive and collectively exhaustive, what is the probability that one or
the other occurs?
a. 0.00
b. 0.50
c. 1.00
d. Cannot be determined from the information given.
ANS: C
PTS: 1
REF: SECTION 6.1
16. If events A and B are mutually exclusive and collectively exhaustive, what is the probability that event
A occurs?
a. 0.25
b. 0.50
c. 1.00
d. Cannot be determined from the information given.
ANS: D
PTS: 1
REF: SECTION 6.1
17. If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the
probability that event A occurs?
a. 0.00
b. 0.50
c. 1.00
d. Cannot be determined from the information given.
ANS: B
PTS: 1
REF: SECTION 6.1
18. If event A and event B cannot occur at the same time, then A and B are said to be
a. mutually exclusive
b. independent
c. collectively exhaustive
d. None of these choices.
ANS: A
PTS: 1
REF: SECTION 6.1
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copied, or distributed without the prior consent of the publisher.
19. The collection of all possible events is called
a. an outcome
b. a sample space
c. an event
d. None of these choices.
ANS: B
PTS: 1
REF: SECTION 6.1
TRUE/FALSE
20. P(A) + P(B) = 1 for any events A and B that are mutually exclusive.
ANS: F
PTS: 1
REF: SECTION 6.1
21. The relative frequency approach to probability uses long term frequencies, often based on past data.
ANS: T
PTS: 1
REF: SECTION 6.1
22. Predicting the outcome of a football game is using the subjective approach to probability.
ANS: T
PTS: 1
REF: SECTION 6.1
23. You think you have a 90% chance of passing your next advanced financial accounting exam. This is
an example of subjective approach to probability.
ANS: T
PTS: 1
REF: SECTION 6.1
24. The collection of all the possible outcomes of a random experiment is called a sample space.
ANS: T
PTS: 1
REF: SECTION 6.1
25. If events A and B cannot occur at the same time, they are called mutually exclusive.
ANS: T
PTS: 1
REF: SECTION 6.1
26. If either event A or event B must occur, they are called mutually exclusive.
ANS: F
PTS: 1
REF: SECTION 6.1
27. If either event A or event B must occur, then A and B are mutually exclusive and collectively
exhaustive events.
ANS: T
PTS: 1
REF: SECTION 6.1
28. If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive.
ANS: F
PTS: 1
REF: SECTION 6.1
29. If P(A) = 0.4 and P(B) = 0.6, then A and B must be mutually exclusive.
ANS: F
PTS: 1
REF: SECTION 6.1
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copied, or distributed without the prior consent of the publisher.
COMPLETION
30. A random experiment is an action or process that leads to one of several possible
____________________.
ANS: outcomes
PTS: 1
REF: SECTION 6.1
31. The outcomes of a sample space must be ____________________, which means that all possible
outcomes must be included.
ANS: exhaustive
PTS: 1
REF: SECTION 6.1
32. The outcomes of a sample space must be ____________________, which means that no two outcomes
can occur at the same time.
ANS: mutually exclusive
PTS: 1
REF: SECTION 6.1
33. A(n) ____________________ of a random experiment is a list of all possible outcomes of the
experiment.
ANS: sample space
PTS: 1
REF: SECTION 6.1
34. The outcomes of a sample space must be ____________________ and ____________________.
ANS:
exhaustive; mutually exclusive
mutually exclusive; exhaustive
PTS: 1
REF: SECTION 6.1
35. There are ____________________ requirements of probabilities for the outcomes of a sample space.
ANS:
two
2
PTS: 1
REF: SECTION 6.1
36. An individual outcome of a sample space is called a(n) ____________________ event.
ANS: simple
PTS: 1
REF: SECTION 6.1
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copied, or distributed without the prior consent of the publisher.
37. A(n) ____________________ is a collection or set of one or more simple events in a sample space.
ANS: event
PTS: 1
REF: SECTION 6.1
38. The probability of an event is the ____________________ of the probabilities of the simple events
that constitute the event.
ANS: sum
PTS: 1
REF: SECTION 6.1
39. No matter which approach was used to assign probability (classical, relative frequency, or subjective)
the one that is always used to interpret a probability is the ____________________ approach.
ANS: relative frequency
PTS: 1
REF: SECTION 6.1
SHORT ANSWER
40. Abby, Bianca, and Cameron, three candidates for the presidency of a college's student body, are to
address a student forum. The forum's organizer is to select the order in which the candidates will give
their speeches, and must do so in such a way that each possible order is equally likely to be selected.
a.
b.
c.
d.
e.
What is the random experiment?
List the outcomes in the sample space.
Assign probabilities to the outcomes.
What is the probability that Cameron will speak first?
What is the probability that Abby will speak before Cameron does?
ANS:
a.
b.
c.
d.
e.
The random experiment is to observe the order in which the three candidates give their
speeches.
S = {ABC, ACB, BAC, BCA, CAB, CBA}, where A = Abby, B = Bianca, and C = Cameron.
The probability assigned to each outcome is 1/6.
P(CAB, CBA) = 1/3
P(ABC, ACB, BAC) = 1/2
PTS: 1
REF: SECTION 6.1
41. There are three approaches to determining the probability that an outcome will occur: classical,
relative frequency, and subjective. For each situation that follows, determine which approach is most
appropriate.
a.
b.
c.
An American will win the French Open Tennis Tournament next year.
The probability of getting any single number on a balanced die is 1/6.
Based on the past, it's reasonable to assume the average book sales for a certain textbook
is 5,000 copies per month.
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copied, or distributed without the prior consent of the publisher.
ANS:
a. subjective
b. classical
c. relative frequency
PTS: 1
REF: SECTION 6.1
Appliance Store Sales
Sales records of an appliance store showed the following number of dishwashers sold weekly for each
of the last 50 weeks.
Number of
Dishwashers Sold
0
1
2
3
4
Number of Weeks
20
15
10
4
1
42. {Appliance Store Sales Narrative} Define the random experiment of interest to the store.
ANS:
The random experiment consists of observing the number of dishwashers sold in any given week.
PTS: 1
REF: SECTION 6.1
43. {Appliance Store Sales Narrative} List the outcomes in the sample space.
ANS:
S = {0, 1, 2, 3, 4}
PTS: 1
REF: SECTION 6.1
44. {Appliance Store Sales Narrative} What approach would you use in determining the probabilities for
next week's sales? Assign probabilities to the outcomes.
ANS:
The relative frequency approach was used.
Number of
Dishwashers
0
1
2
3
4
PTS: 1
Prob.
0.40
0.30
0.20
0.08
0.02
REF: SECTION 6.1
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copied, or distributed without the prior consent of the publisher.
45. {Appliance Store Sales Narrative} What is the probability of selling at least two dishwashers in any
given week?
ANS:
P{2, 3, 4} = 0.30
PTS: 1
REF: SECTION 6.1
46. {Appliance Store Sales Narrative} What is the probability of selling between 1 and 3 (inclusive)
dishwashers in any given week?
ANS:
P{1,2,3} = 0.58
PTS: 1
REF: SECTION 6.1
Stock's Price
An investor estimates that there is a 75% chance that a particular stock's price will increase to $100 per
share over the next three weeks, based past data.
47. {Stock's Price Narrative} Which approach was used to produce this figure?
ANS:
The relative frequency approach
PTS: 1
REF: SECTION 6.1
48. {Stock's Price Narrative} Interpret the 75% probability.
ANS:
We interpret the 75% figure to mean that if we had an infinite number of stocks with exactly the same
economic and market characteristics as the one the investor will buy, 75% of them will increase in
price to $100 over the next three weeks.
PTS: 1
REF: SECTION 6.1
49. The sample space of the toss of a balanced coin is S = {1, 2, 3, 4, 5, 6}. If the die is balanced, each
simple event (outcome) has the same probability. Find the probability of the following events:
a.
b.
c.
d.
Rolling an odd number
Rolling a number less than or equal to 3
Rolling a number greater than or equal to 5
Rolling a number between 2 and 5, inclusive.
ANS:
a. 3/6
b. 3/6
c. 2/6
d. 4/6
PTS: 1
REF: SECTION 6.1
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copied, or distributed without the prior consent of the publisher.
Interest Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a home
loan based on a 30-year mortgage, based on past records.
Interest Rate
Probability
6.0%
0.20
6.5%
0.23
7.0%
0.25
7.5%
0.28
>7.5%
.04
50. {Interest Rates Narrative} If a bank is selected at random from this distribution, what is the probability
that the interest rate charged on a home loan exceeds 7.0%?
ANS:
0.32
PTS: 1
REF: SECTION 6.1
51. {Interest Rates Narrative} What is the most common interest rate?
ANS:
7.5%, since it occurred 28% of the time.
PTS: 1
REF: SECTION 6.1
52. {Interest Rates Narrative} What approach was used in estimating the probabilities for the interest
rates?
ANS:
relative frequency approach
PTS: 1
REF: SECTION 6.1
This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.