Description
Essentials of Modern Business Statistics with Microsoft Excel 6th Edition by David R. Anderson – Test Bank
Sample Questions
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Chapter_2_Descriptive_Statistics_Tabular_and_Graphical_Displays (1)
Multiple Choice 
1. The minimum number of variables represented in a bar chart is

2. The minimum number of variables represented in a histogram is

3. Which of the following graphical methods is most appropriate for categorical data?

a. 
ogive 

b. 
pie chart 

c. 
histigram 

d. 
scatter diagram 

4. In a stemandleaf display,

a. 
a single digit is used to define each stem, and a single digit is used to define each leaf 

b. 
a single digit is used to define each stem, and one or more digits are used to define each leaf 

c. 
one or more digits are used to define each stem, and a single digit is used to define each leaf 

d. 
one or more digits are used to define each stem, and one or more digits are used to define each leaf 

5. A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a

a. 
relative frequency distribution 

b. 
pie chart 

c. 
stemandleaf display 

d. 
pivot table 

6. The proper way to construct a stemandleaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to

a. 
exclude a stem labeled ‘8’ 

b. 
include a stem labeled ‘8’ and enter no leaves on the stem 

c. 
include a stem labeled ‘(8)’ and enter no leaves on the stem 

d. 
include a stem labeled ‘8’ and enter one leaf value of ‘0’ on the stem 

7. Data that provide labels or names for groupings of like items are known as

a. 
categorical data 

b. 
quantitative data 

c. 
label data 

d. 
generic data 

8. A researcher is gathering data from four geographical areas designated: South = 1; North = 2; East = 3; West = 4. The designated geographical regions represent

a. 
categorical data 

b. 
quantitative data 

c. 
directional data 

d. 
either quantitative or categorical data 

9. Data that indicate how much or how many are know as

a. 
categorical data 

b. 
quantitative data 

c. 
label data 

d. 
category data 

10. The ages of employees at a company represent

a. 
categorical data 

b. 
quantitative data 

c. 
label data 

d. 
time series data 

11. A frequency distribution is

a. 
a tabular summary of a set of data showing the fraction of items in each of several nonoverlapping classes 

b. 
a graphical form of representing data 

c. 
a tabular summary of a set of data showing the number of items in each of several nonoverlapping classes 

d. 
a graphical device for presenting categorical data 

12. The sum of frequencies for all classes will always equal

a. 
1 

b. 
the number of elements in a data set 

c. 
the number of classes 

d. 
a value between 0 and 1 

13. In constructing a frequency distribution, as the number of classes are decreased, the class width

a. 
decreases 

b. 
remains unchanged 

c. 
increases 

d. 
can increase or decrease depending on the data values 

14. If several frequency distributions are constructed from the same data set, the distribution with the widest class width will have the

a. 
fewest classes 

b. 
most classes 

c. 
same number of classes as the other distributions since all are constructed from the same data 

d. 
None of the other answers are correct. 

15. Excel’s __________ can be used to construct a frequency distribution for categorical data.

a. 
DISTRIBUTION function 

b. 
SUM function 

c. 
FREQUENCY function 

d. 
COUNTIF function 

16. A tabular summary of a set of data showing the fraction of the total number of items in several nonoverlapping classes is a

a. 
frequency distribution. 

b. 
relative frequency distribution. 

c. 
frequency. 

d. 
cumulative frequency distribution. 

17. The relative frequency of a class is computed by

a. 
dividing the midpoint of the class by the sample size. 

b. 
dividing the frequency of the class by the midpoint. 

c. 
dividing the sample size by the frequency of the class. 

d. 
dividing the frequency of the class by the sample size. 

18. The sum of the relative frequencies for all classes will always equal

a. 
the sample size 

b. 
the number of classes 

c. 
one 

d. 
100 

19. A tabular summary of data showing the percentage of items in each of several nonoverlapping classes is a

a. 
frequency distribution 

b. 
relative frequency distribution 

c. 
percent frequency distribution 

d. 
cumulative percent frequency distribution 

20. The percent frequency of a class is computed by

a. 
multiplying the relative frequency by 10 

b. 
dividing the relative frequency by 100 

c. 
multiplying the relative frequency by 100 

d. 
adding 100 to the relative frequency 

21. The sum of the percent frequencies for all classes will always equal

a. 
one 

b. 
the number of classes 

c. 
the number of items in the study 

d. 
100 

22. In a cumulative frequency distribution, the last class will always have a cumulative frequency equal to

a. 
one 

b. 
100% 

c. 
the total number of elements in the data set 

d. 
None of the other answers are correct. 

23. In a cumulative relative frequency distribution, the last class will have a cumulative relative frequency equal to

a. 
one 

b. 
zero 

c. 
100 

d. 
None of the other answers are correct. 

24. In a cumulative percent frequency distribution, the last class will have a cumulative percent frequency equal to

a. 
one 

b. 
100 

c. 
the total number of elements in the data set 

d. 
None of the other answers are correct. 

25. The difference between the lower class limits of adjacent classes provides the

a. 
number of classes 

b. 
class limits 

c. 
class midpoint 

d. 
class width 

Exhibit 21
The numbers of hours worked (per week) by 400 statistics students are shown below.

Number of hours 
Frequency 

0 − 9 
20 

10 − 19 
80 

20 − 29 
200 

30 − 39 
100 

26. Refer to Exhibit 21. The class width for this distribution

a. 
is 9 

b. 
is 10 

c. 
is 39, which is: the largest value minus the smallest value or 39 − 0 = 39 

d. 
varies from class to class 

27. Refer to Exhibit 21. The midpoint of the last class is

a. 
50 

b. 
34 

c. 
35 

d. 
34.5 

28. Refer to Exhibit 21. The number of students working 19 hours or less

a. 
is 80 

b. 
is 100 

c. 
is 180 

d. 
is 300 

29. Refer to Exhibit 21. The relative frequency of students working 9 hours or less

a. 
is 20 

b. 
is 100 

c. 
is 0.95 

d. 
0.05 

30. Refer to Exhibit 21. The cumulative relative frequency for the class of 20 − 29

a. 
is 300 

b. 
is 0.25 

c. 
is 0.75 

d. 
is 0.5 

31. Refer to Exhibit 21. The percentage of students working 10 − 19 hours is

a. 
20% 

b. 
25% 

c. 
75% 

d. 
80% 

32. Refer to Exhibit 21. The percentage of students working 19 hours or less is

a. 
20% 

b. 
25% 

c. 
75% 

d. 
80% 

33. Refer to Exhibit 21. The cumulative percent frequency for the class of 30 − 39 is

a. 
100% 

b. 
75% 

c. 
50% 

d. 
25% 

34. Refer to Exhibit 21. The cumulative frequency for the class of 20 − 29

a. 
is 200 

b. 
is 300 

c. 
is 0.75 

d. 
is 0.50 

35. Refer to Exhibit 21. If a cumulative frequency distribution is developed for the above data, the last class will have a cumulative frequency of

a. 
100 

b. 
1 

c. 
30 − 39 

d. 
400 

36. Refer to Exhibit 21. The percentage of students who work at least 10 hours per week is

a. 
50% 

b. 
5% 

c. 
95% 

d. 
100% 

Exhibit 22
Information on the type of industry is provided for a sample of 50 Fortune 500 companies.

Industry Type 
Frequency 

Banking 
7 

Consumer Products 
15 

Electronics 
10 

Retail 
18 

37. Refer to Exhibit 22. The number of industries that are classified as retail is

a. 
32 

b. 
18 

c. 
0.36 

d. 
36% 

38. Refer to Exhibit 22. The relative frequency of industries that are classified as banking is

a. 
7 

b. 
0.07 

c. 
0.70 

d. 
0.14 

39. Refer to Exhibit 22. The percent frequency of industries that are classified as electronics is

a. 
10 

b. 
20 

c. 
0.10 

d. 
0.20 

Exhibit 23
The number of sick days taken (per month) by 200 factory workers is summarized below.

Number of Days 
Frequency 

0 − 5 
120 

6 − 10 
65 

11 − 15 
14 

16 − 20 
1 

40. Refer to Exhibit 23. The class width for this distribution

a. 
is 5 

b. 
is 6 

c. 
is 20, which is: the largest value minus the smallest value or 20 − 0 = 20 

d. 
varies from class to class 

41. Refer to Exhibit 23. The midpoint of the first class is

42. Refer to Exhibit 23. The number of workers who took less than 11 sick days per month

a. 
was 15 

b. 
was 200 

c. 
was 185 

d. 
was 65 

43. Refer to Exhibit 23. The number of workers who took at most 10 sick days per month

a. 
was 15 

b. 
was 200 

c. 
was 185 

d. 
was 65 

44. Refer to Exhibit 23. The number of workers who took more than 10 sick days per month

a. 
was 15 

b. 
was 200 

c. 
was 185 

d. 
was 65 

45. Refer to Exhibit 23. The number of workers who took at least 11 sick days per month

a. 
was 15 

b. 
was 200 

c. 
was 185 

d. 
was 65 

46. Refer to Exhibit 23. The relative frequency of workers who took 10 or fewer sick days

a. 
was 185 

b. 
was 0.925 

c. 
was 93 

d. 
was 15 

47. Refer to Exhibit 23. The cumulative relative frequency for the class of 11 − 15

a. 
is 199 

b. 
is 0.07 

c. 
is 1 

d. 
is 0.995 

48. Refer to Exhibit 23. The percentage of workers who took 0 – 5 sick days per month was

a. 
20% 

b. 
120% 

c. 
75% 

d. 
60% 

49. Refer to Exhibit 23. The cumulative percent frequency for the class of 16 − 20 is

a. 
100% 

b. 
65% 

c. 
92.5% 

d. 
0.5% 

50. Refer to Exhibit 23. The cumulative frequency for the class of 11 − 15

a. 
is 200 

b. 
is 14 

c. 
is 199 

d. 
is 1 

Exhibit 24
A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school.


Undergraduate Major 



Graduate School 
Business 
Engineering 
Others 
Total 

Yes 
35 
42 
63 
140 

No 
91 
104 
65 
260 

Total 
126 
146 
128 
400 

51. Refer to Exhibit 24. What percentage of the students does not plan to go to graduate school?

a. 
280 

b. 
520 

c. 
65 

d. 
32 

52. Refer to Exhibit 24. What percentage of the students’ undergraduate major is engineering?

a. 
292 

b. 
520 

c. 
65 

d. 
36.5 

53. Refer to Exhibit 24. Of those students who are majoring in business, what percentage plans to go to graduate school?

a. 
27.78 

b. 
8.75 

c. 
70 

d. 
72.22 

54. Refer to Exhibit 24. Among the students who plan to go to graduate school, what percentage indicated “Other” majors?

a. 
15.75 

b. 
45 

c. 
54 

d. 
35 

55. A graphical device for depicting categorical data that have been summarized in a frequency distribution, relative frequency distribution, or percent frequency distribution is a(n)

a. 
histogram 

b. 
stemandleaf display 

c. 
ogive 

d. 
bar chart 

56. A graphical device for presenting categorical data summaries based on subdivision of a circle into sectors that correspond to the relative frequency for each class is a

a. 
histogram 

b. 
stemandleaf display 

c. 
pie chart 

d. 
bar chart 

57. Categorical data can be graphically represented by using a(n)

a. 
histogram 

b. 
frequency polygon 

c. 
ogive 

d. 
bar chart 

58. Fifteen percent of the students in a School of Business Administration are majoring in Economics, 20% in Finance, 35% in Management, and 30% in Accounting. The graphical device(s) that can be used to present these data is (are)

a. 
a line graph 

b. 
only a bar chart 

c. 
only a pie chart 

d. 
both a bar chart and a pie chart 

59. Methods that use simple arithmetic and easytodraw graphs to summarize data quickly are called

a. 
exploratory data analysis 

b. 
relative frequency distributions 

c. 
bar charts 

d. 
pie charts 

60. The total number of data items with a value less than or equal to the upper limit for the class is given by the

a. 
frequency distribution 

b. 
relative frequency distribution 

c. 
cumulative frequency distribution 

d. 
cumulative relative frequency distribution 

61. Excel’s __________ can be used to construct a frequency distribution for quantitative data.

a. 
COUNTIF function 

b. 
SUM function 

c. 
PivotTable Report 

d. 
AVERAGE function 

62. A graphical presentation of a frequency distribution, relative frequency distribution, or percent frequency distribution of quantitative data constructed by placing the class intervals on the horizontal axis and the frequencies on the vertical axis is a

a. 
histogram 

b. 
bar chart 

c. 
stemandleaf display 

d. 
pie chart 

63. A common graphical presentation of quantitative data is a

a. 
histogram 

b. 
bar chart 

c. 
relative frequency 

d. 
pie chart 

64. When using Excel to create a __________ one must edit the chart to remove the gaps between rectangles.

a. 
scatter diagram 

b. 
bar chart 

c. 
histogram 

d. 
pie chart 

65. A __________ can be used to graphically present quantitative data.

a. 
histogram 

b. 
pie chart 

c. 
stemandleaf display 

d. 
both a histogram and a stemandleaf display are correct 

66. A(n) __________ is a graph of a cumulative distribution.

a. 
histogram 

b. 
pie chart 

c. 
stemandleaf display 

d. 
ogive 

67. Excel’s Chart Tools can be used to construct a

a. 
bar chart 

b. 
pie chart 

c. 
histogram 

d. 
All of these can be constructed using Excel’s Chart Tools. 

68. To construct a bar chart using Excel’s Chart Tools, choose __________ as the chart type.

a. 
column 

b. 
pie 

c. 
scatter 

d. 
line 

69. To construct a pie chart using Excel’s Chart Tools, choose __________ as the chart type.

a. 
column 

b. 
pie 

c. 
scatter 

d. 
line 

70. To construct a histogram using Excel’s Chart Tools, choose __________ as the chart type.

a. 
column 

b. 
pie 

c. 
scatter 

d. 
line 

71. Excel’s Chart Tools does not have a chart type for constructing a

a. 
bar chart 

b. 
pie chart 

c. 
histogram 

d. 
stemandleaf display 

72. A tabular method that can be used to summarize the data on two variables simultaneously is called

a. 
simultaneous equations 

b. 
a crosstabulation 

c. 
a histogram 

d. 
a dot plot 

73. Excel’s __________ can be used to construct a crosstabulation.

a. 
Chart Tools 

b. 
SUM function 

c. 
PivotTable Report 

d. 
COUNTIF function 

74. In a crosstabulation

a. 
both variables must be categorical 

b. 
both variables must be quantitative 

c. 
one variable must be categorical and the other must be quantitative 

d. 
either or both variables can be categorical or quantitative 

75. A graphical presentation of the relationship between two quantitative variables is

a. 
a pie chart 

b. 
a histogram 

c. 
a crosstabulation 

d. 
a scatter diagram 

76. Excel’s __________ can be used to construct a scatter diagram.

a. 
Chart Tools 

b. 
SUM function 

c. 
CROSSTAB function 

d. 
RAND function 

77. 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 

c. 
Simpson’s paradox 

d. 
disaggregation 

78. 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 

79. A histogram is not appropriate for displaying which of the following types of information?

a. 
frequency 

b. 
relative frequency 

c. 
cumulative frequency 

d. 
percent frequency 

80. For stemandleaf displays where the leaf unit is not stated, the leaf unit is assumed to equal

a. 
0 

b. 
.1 

c. 
1 

d. 
10 

81. Which of the following graphical methods is not intended for quantitative data?

a. 
ogive 

b. 
dot plot 

c. 
scatter diagram 

d. 
pie chart 

82. Which of the following is least useful in studying the relationship between two variables?

a. 
trendline 

b. 
stemandleaf display 

c. 
crosstabulation 

d. 
scatter diagram 

83. The sum of the relative frequencies in any relative frequency distribution always equals

a. 
the number of observation 

b. 
1.00 

c. 
100 

d. 
the number of variables 

84. The sum of the frequencies in any frequency distribution always equals

a. 
the number of observations 

b. 
1.00 

c. 
100 

d. 
the number of variables 

85. In quality control applications, bar charts are used to identify the most important causes of problems. When the bars are arranged in descending order of height from left to right with the most frequently occurring cause appearing first, the bar chart is called a

a. 
causeandeffect diagram 

b. 
histogram 

c. 
Pareto diagram 

d. 
ogive 

86. A graphical tool typically associated with the display of key performance indicators is a

a. 
sidebyside bar chart 

b. 
stemandleaf display 

c. 
dot plot 

d. 
data dashboard 

87. The approximately class width for a frequency distribution involving quantitative data can be determined using the expression

a. 
mean frequency ÷ total frequency 

b. 
total frequency ÷ class midpoint 

c. 
range ÷ desired number of classes 

d. 
desired number of classes ÷ class midpoint 

88. A display used to compare the relative frequency or percent frequency of two categorical variables is a

a. 
sidebyside bar chart 

b. 
stacked bar chart 

c. 
pie chart 

d. 
stemandleaf display 

89. Thirty students in the School of Business were asked what their majors were. The following represents their responses (M = Management; A = Accounting; E = Economics; O = Others).

A 
M 
M 
A 
M 
M 
E 
M 
O 
A 

E 
E 
M 
A 
O 
E 
M 
A 
M 
A 

M 
A 
O 
A 
M 
E 
E 
M 
A 
M 
a. 
Construct a frequency distribution and a bar chart. 
b. 
Construct a relative frequency distribution and a pie chart. 
ANSWER: 

a. and b. 



Major 
Frequency 
Relative Frequency 


M 
12 
0.4 


A 
9 
0.3 


E 
6 
0.2 


O 
3 
0.1 


Total 
30 
1.0 


POINTS: 
1 

Chapter_4_Introduction_to_Probability (1)
Multiple Choice 
1. 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 

2. Revised probabilities of events based on additional information are

a. 
joint probabilities 

b. 
posterior probabilities 

c. 
marginal probabilities 

d. 
complementary probabilities 

3. Posterior probabilities are computed using

a. 
the classical method 

b. 
Chebyshev’s theorem 

c. 
the empirical rule 

d. 
Bayes’ theorem 

4. The complement of P(A  B) is

a. 
P(A^{C}  B) 

b. 
P(A  B^{C}) 

c. 
P(B  A) 

d. 
P(A I B) 

5. An element of the sample space is

a. 
an event 

b. 
an estimator 

c. 
a sample point 

d. 
an outlier 

6. The probability of an intersection of two events is computed using the

a. 
addition law 

b. 
subtraction law 

c. 
multiplication law 

d. 
division law 

7. If A and B are mutually exclusive, then

a. 
P(A) + P(B) = 0 

b. 
P(A) + P(B) = 1 

c. 
P(A I B) = 0 

d. 
P(A I B) = 1 

8. Posterior probabilities are

a. 
simple probabilities 

b. 
marginal probabilities 

c. 
joint probabilities 

d. 
conditional probabilities 

9. 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 

10. Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is

a. 
much larger than one 

b. 
zero 

c. 
infinity 

d. 
None of the other answers is correct. 

11. Any process that generates welldefined outcomes is

a. 
an event 

b. 
an experiment 

c. 
a sample point 

d. 
None of the other answers is correct. 

12. In statistical experiments, each time the experiment is repeated

a. 
the same outcome must occur 

b. 
the same outcome can not occur again 

c. 
a different outcome may occur 

d. 
None of the other answers is correct. 

13. Each individual outcome of an experiment is called

a. 
the sample space 

b. 
a sample point 

c. 
an experiment 

d. 
an individual 

14. A sample point refers to a(n)

a. 
numerical measure of the likelihood of the occurrence of an event 

b. 
set of all possible experimental outcomes 

c. 
individual outcome of an experiment 

d. 
All of these answers are correct. 

15. The collection of all possible sample points in an experiment is

a. 
the sample space 

b. 
a sample point 

c. 
an experiment 

d. 
the population 

16. The set of all possible sample points (experimental outcomes) is called

a. 
a sample 

b. 
an event 

c. 
the sample space 

d. 
a population 

17. The sample space refers to

a. 
any particular experimental outcome 

b. 
the sample size minus one 

c. 
the set of all possible experimental outcomes 

d. 
both any particular experimental outcome and the set of all possible experimental outcomes are correct 

18. An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is

19. An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is

20. A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is

a. 
30 

b. 
100 

c. 
729 

d. 
1,000 

21. 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

22. Assume your favorite football team has 2 games left to finish the season. The outcome of each game can be win, lose or tie. The number of possible outcomes is

a. 
2 

b. 
4 

c. 
6 

d. 
None of the other answers is correct. 

23. Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 3 customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is

24. A graphical device used for enumerating sample points in a multiplestep experiment is a

a. 
bar chart 

b. 
pie chart 

c. 
histogram 

d. 
None of the other answers is correct. 

25. Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there?

26. The “Top Three” at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many “Top Three” outcomes are there?

a. 
302,400 

b. 
720 

c. 
1,814,400 

d. 
10 

27. When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the

a. 
relative frequency method 

b. 
subjective method 

c. 
probability method 

d. 
classical method 

28. A method of assigning probabilities that assumes the experimental outcomes are equally likely is referred to as the

a. 
objective method 

b. 
classical method 

c. 
subjective method 

d. 
experimental method 

29. 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 

30. 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 other answers is correct. 

31. 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. 
1.00 

d. 
0.75 

32. The probability assigned to each experimental outcome must be

a. 
any value larger than zero 

b. 
smaller than zero 

c. 
one 

d. 
between zero and one 

33. An experiment consists of four outcomes with P(E_{1}) = 0.2, P(E_{2}) = 0.3, and P(E_{3}) = 0.4. The probability of outcome E_{4} is

a. 
0.500 

b. 
0.024 

c. 
0.100 

d. 
0.900 

34. A graphical method of representing the sample points of a multiplestep experiment is

a. 
a frequency polygon 

b. 
a histogram 

c. 
an ogive 

d. 
a tree diagram 

35. 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 

36. A(n) __________ is a collection of sample points.

a. 
probability 

b. 
permutation 

c. 
experiment 

d. 
event 

37. Given that event E has a probability of 0.25, the probability of the complement of event E

a. 
cannot be determined with the above information 

b. 
can have any value between zero and one 

c. 
must be 0.75 

d. 
is 0.25 

38. The symbol ∪ shows the

a. 
union of events 

b. 
intersection of events 

c. 
sum of the probabilities of events 

d. 
sample space 

39. 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 

40. The probability of the union of two events with nonzero probabilities

a. 
cannot be less than one 

b. 
cannot be one 

c. 
cannot be less than one and cannot be one 

d. 
None of the other answers is correct. 

41. The symbol ∩ shows the

a. 
union of events 

b. 
intersection of events 

c. 
sum of the probabilities of events 

d. 
None of the other answers is correct. 

42. The addition law is potentially helpful when we are interested in computing the probability of

a. 
independent events 

b. 
the intersection of two events 

c. 
the union of two events 

d. 
conditional events 

43. If P(A) = 0.38, P(B) = 0.83, and P(A ∩ B) = 0.57; then P(A ∪ B) =

a. 
1.21 

b. 
0.64 

c. 
0.78 

d. 
1.78 

44. If P(A) = 0.62, P(B) = 0.47, and P(A ∪ B) = 0.88; then P(A ∩ B) =

a. 
0.2914 

b. 
1.9700 

c. 
0.6700 

d. 
0.2100 

45. If P(A) = 0.85, P(A ∪ B) = 0.72, and P(A ∩ B) = 0.66, then P(B) =

a. 
0.15 

b. 
0.53 

c. 
0.28 

d. 
0.15 

46. Two events are mutually exclusive if

a. 
the probability of their intersection is 1 

b. 
they have no sample points in common 

c. 
the probability of their intersection is 0.5 

d. 
the probability of their intersection is 1 and they have no sample points in common 

47. Events that have no sample points in common are

a. 
independent events 

b. 
posterior events 

c. 
mutually exclusive events 

d. 
complements 

48. The probability of the intersection of two mutually exclusive events

a. 
can be any value between 0 to 1 

b. 
must always be equal to 1 

c. 
must always be equal to 0 

d. 
can be any positive value 

49. If two events are mutually exclusive, then the probability of their intersection

a. 
will be equal to zero 

b. 
can have any value larger than zero 

c. 
must be larger than zero, but less than one 

d. 
will be one 

50. Two events, A and B, are mutually exclusive and each has a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is

a. 
one 

b. 
any positive value 

c. 
zero 

d. 
any value between 0 to 1 

51. 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 

c. 
0.00 

d. 
0.20 

52. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∪ B) =

a. 
0.00 

b. 
0.15 

c. 
0.8 

d. 
0.2 

53. In an experiment, events A and B are mutually exclusive. If P(A) = 0.6, then the probability of B

a. 
cannot be larger than 0.4 

b. 
can be any value greater than 0.6 

c. 
can be any value between 0 to 1 

d. 
cannot be determined with the information given 

54. Which of the following statements is(are) always true?

a. 
1 ≤ P(E_{i}) ≤ 1 

b. 
P(A) = 1 − P(A^{c}) 

c. 
P(A) + P(B) = 1 

d. 
both P(A) = 1 − P(A^{c}) and P(A) + P(B) = 1 

55. One of the basic requirements of probability is

a. 
for each experimental outcome E_{i}, we must have P(E_{i}) ≥ 1 

b. 
P(A) = P(A^{c}) − 1 

c. 
if there are k experimental outcomes, then P(E_{1}) + P(E_{2}) + … + P(E_{k}) = 1 

d. 
both P(A) = P(A^{c}) − 1 and if there are k experimental outcomes, then P(E_{1}) + P(E_{2}) + … + P(E_{k}) = 1 

56. Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.2. The probability of the complement of Event B equals

a. 
0.00 

b. 
0.06 

c. 
0.7 

d. 
None of the other answers is correct. 

57. The multiplication law is potentially helpful when we are interested in computing the probability of

a. 
mutually exclusive events 

b. 
the intersection of two events 

c. 
the union of two events 

d. 
None of the other answers is correct. 

58. If P(A) = 0.80, P(B) = 0.65, and P(A ∪ B) = 0.78, then P(B∩A) =

a. 
0.6700 

b. 
0.8375 

c. 
0.9750 

d. 
Not enough information is given to answer this question. 

59. If two events are independent, then

a. 
they must be mutually exclusive 

b. 
the sum of their probabilities must be equal to one 

c. 
the probability of their intersection must be zero 

d. 
None of the other answers is correct. 

60. If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then P(A∩B) =

a. 
0.209 

b. 
0.000 

c. 
0.550 

d. 
None of the other answers is correct. 

61. If X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then P(X⏐Y) =

a. 
0.0944 

b. 
0.6150 

c. 
1.0000 

d. 
0.0000 

62. Two events with nonzero probabilities

a. 
can be both mutually exclusive and independent 

b. 
cannot be both mutually exclusive and independent 

c. 
are always mutually exclusive 

d. 
cannot be both mutually exclusive and independent and are always mutually exclusive 

63. If P(A) = 0.50, P(B) = 0.60, and P(A ∩ B) = 0.30; then events A and B are

a. 
mutually exclusive events 

b. 
not independent events 

c. 
independent events 

d. 
Not enough information is given to answer this question. 

64. On a December day, the probability of snow is .30. The probability of a “cold” day is .50. The probability of snow and a “cold” day is .15. Are snow and “cold” weather independent events?

a. 
only if given that it snowed 

b. 
no 

c. 
yes 

d. 
only when they are also mutually exclusive 

65. If P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B) is

a. 
0.00 

b. 
0.25 

c. 
1.00 

d. 
cannot be determined from the information given 

66. If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A ∩ B) =

a. 
0.76 

b. 
1.00 

c. 
0.24 

d. 
0.2 

67. If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A ∪ B) =

a. 
0.62 

b. 
0.12 

c. 
0.60 

d. 
0.68 

68. If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then P(A ∪ B) =

a. 
0.65 

b. 
0.55 

c. 
0.10 

d. 
Not enough information is given to answer this question. 

69. 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) 

70. If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A⏐B) =

a. 
0.05 

b. 
0.0325 

c. 
0.65 

d. 
0.8 

71. A sixsided die is tossed 3 times. The probability of observing three ones in a row is

a. 
1/3 

b. 
1/6 

c. 
1/27 

d. 
1/216 

72. If a coin is tossed three times, the likelihood of obtaining three heads in a row is

a. 
zero 

b. 
0.500 

c. 
0.875 

d. 
0.125 

73. If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is

a. 
zero 

b. 
1/32 

c. 
0.5 

d. 
larger than the probability of tails 

74. If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is

a. 
smaller than the probability of tails 

b. 
larger than the probability of tails 

c. 
1/16 

d. 
None of the other answers is correct. 

75. A perfectly balanced coin is tossed 6 times and tails appears on all six tosses. Then, on the seventh trial

a. 
tails cannot appear 

b. 
heads has a larger chance of appearing than tails 

c. 
tails has a better chance of appearing than heads 

d. 
None of the other answers is correct. 

76. The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed 2 times and event A did not occur, then on the third trial event A

a. 
must occur 

b. 
may occur 

c. 
could not occur 

d. 
has a 2/3 probability of occurring 

77. Bayes’ theorem is used to compute

a. 
the prior probabilities 

b. 
the union of events 

c. 
both the prior probabilities and the union of events 

d. 
the posterior probabilities 

78. Initial estimates of the probabilities of events are known as

a. 
sets 

b. 
posterior probabilities 

c. 
conditional probabilities 

d. 
prior probabilities 

79.

A 
B 
C 
D 
E 
1 

Prior 
Conditional 
Joint 

2 
Event 
Probability 
Probability 
Probability 

3 
A1 
0.25 
0.31 


For the Excel worksheet above, which of the following formulas would correctly calculate the joint probability for cell D3?

a. 
=SUM(B3:C3) 

b. 
B3+C3 

c. 
B3/C3 

d. 
=B3*C3 

80.

A 
B 
C 
D 
E 
1 

Prior 
Conditional 
Joint 
Posterior 
2 
Event 
Probability 
Probability 
Probability 
Probability 
3 
A1 
0.45 
0.22 
0.099 

4 
A2 
0.55 
0.16 
0.088 

5 



0.187 

For the Excel worksheet above, which of the following formulas would correctly calculate the posterior probability for cell E3?

a. 
=SUM(B3:D3) 

b. 
=D3/$D$5 

c. 
=D5/$D$3 

d. 
B3/C3+D3 

81. If P(A ∩ B) = 0,

a. 
P(A) + P(B) = 1 

b. 
either P(A) = 0 or P(B) = 0 

c. 
A and B are mutually exclusive events 

d. 
A and B are independent events 

82. The probability of an event is

a. 
the sum of the probabilities of the sample points in the event 

b. 
the product of the probabilities of the sample points in the event 

c. 
the minimum of the probabilities of the sample points in the event 

d. 
the maximum of the probabilities of the sample points in the event 

83. If P(AB) = .3,

a. 
P(BA) = .7 

b. 
P(A^{C}B) = .7 

c. 
P(AB^{C}) = .7 

d. 
P(A^{C}B^{C}) = .7 

84. If A and B are independent events with P(A) = .1 and P(B) = .4, then

a. 
P(A ∩ B) = 0 

b. 
P(A ∩ B) = .04 

c. 
P(A ∪ B) = .5 

d. 
P(A ∩ B) = .25 

85. If P(AB) = .3 and P(B) = .8, then

a. 
P(A) = .24 

b. 
P(BA) = .7 

c. 
P(A ∪ B) = .5 

d. 
P(A ∩ B) = .24 

86. If P(A) = .6, P(B) = .3, and P(A ∩ B) = .2, then P(BA) =

a. 
.33 

b. 
.50 

c. 
.67 

d. 
.90 

87. Which of the following is not a valid representation of a probability?

a. 
35% 

b. 
0 

c. 
1.04 

d. 
3/8 

88. 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 

89. Which of the following is not a proper sample space when all undergraduates at a university are considered?

a. 
S = {instate, outofstate} 

b. 
S = {freshmen, sophomores} 

c. 
S = {age under 21, age 21 or over} 

d. 
S = {a major within business, no business major} 

90. 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 

91. 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 

92. 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 

93. All the employees of ABC Company are assigned ID numbers. The ID number consists of the first letter of an employee’s last name, followed by four numbers.
a. 
How many possible different ID numbers are there? 
b. 
How many possible different ID numbers are there for employees whose last name starts with an “A”? 

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