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Essentials of Statistics for Business and Economics 6th Edition By David R. Anderson – Test Bank
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CHAPTER 2—DESCRIPTIVE STATISTICS: TABULAR AND GRAPHICAL PRESENTATIONS
MULTIPLE CHOICE
 A frequency distribution is a tabular summary of data showing the
a.  fraction of items in several classes 
b.  percentage of items in several classes 
c.  relative percentage of items in several classes 
d.  number of items in several classes 
ANS: D PTS: 1 TOP: Descriptive Statistics
 A frequency distribution is
a.  a tabular summary of a set of data showing the relative frequency 
b.  a graphical form of representing data 
c.  a tabular summary of a set of data showing the frequency of items in each of several nonoverlapping classes 
d.  a graphical device for presenting categorical data 
ANS: C PTS: 1 TOP: Descriptive Statistics
 A tabular summary of a set of data showing the fraction of the total number of items in several classes is a
a.  frequency distribution 
b.  relative frequency distribution 
c.  frequency 
d.  cumulative frequency distribution 
ANS: B PTS: 1 TOP: Descriptive Statistics
 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 
ANS: D PTS: 1 TOP: Descriptive Statistics
 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 
ANS: C PTS: 1 TOP: Descriptive Statistics
 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 
ANS: B PTS: 1 TOP: Descriptive Statistics
 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) which can be used to present these data is (are)
a.  a line chart 
b.  only a bar chart 
c.  only a pie chart 
d.  both a bar chart and a pie chart 
ANS: D PTS: 1 TOP: Descriptive Statistics
 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.  label data 
d.  either quantitative or categorical data 
ANS: A PTS: 1 TOP: Descriptive Statistics
 Categorical data can be graphically represented by using a(n)
a.  histogram 
b.  frequency polygon 
c.  ogive 
d.  bar chart 
ANS: D PTS: 1 TOP: Descriptive Statistics
 A cumulative relative frequency distribution shows
a.  the proportion of data items with values less than or equal to the upper limit of each class 
b.  the proportion of data items with values less than or equal to the lower limit of each class 
c.  the percentage of data items with values less than or equal to the upper limit of each class 
d.  the percentage of data items with values less than or equal to the lower limit of each class 
ANS: A PTS: 1 TOP: Descriptive Statistics
 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 
ANS: A PTS: 1 TOP: Descriptive Statistics
 The sum of the relative frequencies for all classes will always equal
a.  the sample size 
b.  the number of classes 
c.  one 
d.  any value larger than one 
ANS: C PTS: 1 TOP: Descriptive Statistics
 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 
ANS: D PTS: 1 TOP: Descriptive Statistics
 The most common graphical presentation of quantitative data is a
a.  histogram 
b.  bar chart 
c.  relative frequency 
d.  pie chart 
ANS: A PTS: 1 TOP: Descriptive Statistics
 The total number of data items with a value less than 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 
ANS: C PTS: 1 TOP: Descriptive Statistics
 The relative frequency of a class is computed by
a.  dividing the cumulative frequency of the class by n 
b.  dividing n by cumulative frequency of the class 
c.  dividing the frequency of the class by n 
d.  dividing the frequency of the class by the number of classes 
ANS: C PTS: 1 TOP: Descriptive Statistics
 In constructing a frequency distribution, the approximate class width is computed as
a.  (largest data value – smallest data value)/number of classes 
b.  (largest data value – smallest data value)/sample size 
c.  (smallest data value – largest data value)/sample size 
d.  largest data value/number of classes 
ANS: A PTS: 1 TOP: Descriptive Statistics
 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 
ANS: C PTS: 1 TOP: Descriptive Statistics
 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 
ANS: D PTS: 1 TOP: Descriptive Statistics
 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 these alternatives is correct. 
ANS: C PTS: 1 TOP: Descriptive Statistics
 In a cumulative relative frequency distribution, the last class will have a cumulative relative frequency equal to
a.  one 
b.  zero 
c.  the total number of elements in the data set 
d.  None of these alternatives is correct. 
ANS: A PTS: 1 TOP: Descriptive Statistics
 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 these alternatives is correct. 
ANS: B PTS: 1 TOP: Descriptive Statistics
 Data that provide labels or names for categories of like items are known as
a.  categorical data 
b.  quantitative data 
c.  label data 
d.  category data 
ANS: A PTS: 1 TOP: Descriptive Statistics
 A tabular method that can be used to summarize the data on two variables simultaneously is called
a.  simultaneous equations 
b.  crosstabulation 
c.  a histogram 
d.  an ogive 
ANS: B PTS: 1 TOP: Descriptive Statistics
 A graphical presentation of the relationship between two variables is
a.  an ogive 
b.  a histogram 
c.  either an ogive or a histogram, depending on the type of data 
d.  a scatter diagram 
ANS: D PTS: 1 TOP: Descriptive Statistics
 A histogram is said to be skewed to the left if it has a
a.  longer tail to the right 
b.  shorter tail to the right 
c.  shorter tail to the left 
d.  longer tail to the left 
ANS: D PTS: 1 TOP: Descriptive Statistics
 When a histogram has a longer tail to the right, it is said to be
a.  symmetrical 
b.  skewed to the left 
c.  skewed to the right 
d.  none of these alternatives is correct 
ANS: C PTS: 1 TOP: Descriptive Statistics
 In a scatter diagram, a line that provides an approximation of the relationship between the variables is known as
a.  approximation line 
b.  trend line 
c.  line of zero intercept 
d.  line of zero slope 
ANS: B PTS: 1 TOP: Descriptive Statistics
 A histogram is
a.  a graphical presentation of a frequency or relative frequency distribution 
b.  a graphical method of presenting a cumulative frequency or a cumulative relative frequency distribution 
c.  the history of data elements 
d.  the same as a pie chart 
ANS: A PTS: 1 TOP: Descriptive Statistics
 A situation in which conclusions based upon aggregated crosstabulation are different from unaggregated crosstabulation is known as
a.  wrong crosstabulation 
b.  Simpson’s rule 
c.  Simpson’s paradox 
d.  aggregated crosstabulation 
ANS: C PTS: 1 TOP: Descriptive Statistics
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 
 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 
ANS: B PTS: 1 TOP: Descriptive Statistics
 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 
ANS: B PTS: 1 TOP: Descriptive Statistics
 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 
ANS: D PTS: 1 TOP: Descriptive Statistics
 Refer to Exhibit 21. The percentage of students working 19 hours or less is
a.  20% 
b.  25% 
c.  75% 
d.  80% 
ANS: B PTS: 1 TOP: Descriptive Statistics
 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 
ANS: C PTS: 1 TOP: Descriptive Statistics
 Refer to Exhibit 21. The cumulative percent frequency for the class of 30 – 39 is
a.  100% 
b.  75% 
c.  50% 
d.  25% 
ANS: A PTS: 1 TOP: Descriptive Statistics
 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 0.5 
ANS: B PTS: 1 TOP: Descriptive Statistics
 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 
ANS: D PTS: 1 TOP: Descriptive Statistics
 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% 
ANS: C PTS: 1 TOP: Descriptive Statistics
 Refer to Exhibit 21. The number of students who work 19 hours or less is
a.  80 
b.  100 
c.  200 
d.  400 
ANS: B PTS: 1 TOP: Descriptive Statistics
 Refer to Exhibit 21. The midpoint of the last class is
a.  50 
b.  34 
c.  35 
d.  34.5 
ANS: D PTS: 1 TOP: Descriptive Statistics
Exhibit 22
A survey of 800 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  70  84  126  280 
No  182  208  130  520 
Total  252  292  256  800 
 Refer to Exhibit 22. What percentage of the students does not plan to go to graduate school?
a.  280 
b.  520 
c.  65 
d.  32 
ANS: C PTS: 1 TOP: Descriptive Statistics
 Refer to Exhibit 22. What percentage of the students’ undergraduate major is engineering?
a.  292 
b.  520 
c.  65 
d.  36.5 
ANS: D PTS: 1 TOP: Descriptive Statistics
 Refer to Exhibit 22. 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 
ANS: A PTS: 1 TOP: Descriptive Statistics
 Refer to Exhibit 22. Among the students who plan to go to graduate school, what percentage indicated “Other” majors?
a.  15.75 
b.  45 
c.  54 
d.  35 
ANS: B PTS: 1 TOP: Descriptive Statistics
Exhibit 23
Michael’s ComputeAll, a national computer retailer, has kept a record of the number of laptop computers they have sold for a period of 80 days. Their sales records are shown below:
Number of Laptops Sold Number of Days
0 – 19 5
20 – 39 15
40 – 59 30
60 – 79 20
80 – 99 10
Total 80
 Refer to Exhibit 23. The class width of the above distribution is
a.  0 to 100 
b.  20 
c.  80 
d.  5 
ANS: B PTS: 1 TOP: Descriptive Statistics
 Refer to Exhibit 23. The lower limit of the first class is
a.  5 
b.  80 
c.  0 
d.  20 
ANS: C PTS: 1 TOP: Descriptive Statistics
 Refer to Exhibit 23. If one develops a cumulative frequency distribution for the above data, the last class will have a frequency of
a.  10 
b.  100 
c.  0 to 100 
d.  80 
ANS: D PTS: 1 TOP: Descriptive Statistics
 Refer to Exhibit 23. The percentage of days in which the company sold at least 40 laptops is
a.  37.5% 
b.  62.5% 
c.  90.0% 
d.  75.0% 
ANS: D PTS: 1 TOP: Descriptive Statistics
 Refer to Exhibit 23. The number of days in which the company sold less than 60 laptops is
a.  20 
b.  30 
c.  50 
d.  60 
ANS: C PTS: 1 TOP: Descriptive Statistics
PROBLEM
 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. 
ANS:
(a)  (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 
PTS: 1 TOP: Descriptive Statistics
 Twenty employees of the Ahmadi Corporation were asked if they liked or disliked the new district manager. Below you are given their responses. Let L represent liked and D represent disliked.
L  L  D  L  D 
D  D  L  L  D 
D  L  D  D  L 
D  D  L  D  L 
a.  Construct a frequency distribution and a bar chart. 
b.  Construct a relative frequency distribution and a pie chart. 
ANS:
a and b
Preferences 
Frequency 
Relative
Frequency 
L  9  0.45 
D  11  0.55 
Total  20  1.00 
PTS: 1 TOP: Descriptive Statistics
 Forty shoppers were asked if they preferred the weight of a can of soup to be 6 ounces, 8 ounces, or 10 ounces. Below you are given their responses.
6  6  6  10  8  8  8  10  6  6 
10  10  8  8  6  6  6  8  6  6 
8  8  8  10  8  8  6  10  8  6 
6  8  8  8  10  10  8  10  8  6 
a.  Construct a frequency distribution and graphically represent the frequency distribution. 
b.  Construct a relative frequency distribution and graphically represent the relative frequency distribution. 
ANS:
a and b
Preferences 
Frequency 
Relative
Frequency 
6 ounces  14  0.350 
8 ounces  17  0.425 
10 ounces  9  0.225 
Total  40  1.000 
PTS: 1 TOP: Descriptive Statistics
 A student has completed 20 courses in the School of Arts and Sciences. Her grades in the 20 courses are shown below.
A  B  A  B  C 
C  C  B  B  B 
B  A  B  B  B 
C  B  C  B  A 
a.  Develop a frequency distribution and a bar chart for her grades. 
b.  Develop a relative frequency distribution for her grades and construct a pie chart. 
ANS:
a and b
Grade 
Frequency 
Relative
Frequency 
A  4  0.20 
B  11  0.55 
C  5  0.25 
Total  20  1.00 
PTS: 1 TOP: Descriptive Statistics
 A sample of 50 TV viewers were asked, “Should TV sponsors pull their sponsorship from programs that draw numerous viewer complaints?” Below are the results of the survey. (Y = Yes; N = No; W = Without Opinion)
N  W  N  N  Y  N  N  N  Y  N 
N  Y  N  N  N  N  N  Y  N  N 
Y  N  Y  W  N  Y  W  W  N  Y 
W  W  N  W  Y  W  N  W  Y  W 
N  Y  N  Y  N  W  Y  Y  N  Y 
a.  Construct a frequency distribution and a bar chart. 
b.  Construct a relative frequency distribution and a pie chart. 
ANS:
a and b
Frequency 
Relative
Frequency 

No  24  0.48 
Yes  15  0.30 
Without Opinion  11  0.22 
Total  50  1.00 
PTS: 1 TOP: Descriptive Statistics
 Below you are given the examination scores of 20 students.
52  99  92  86  84 
63  72  76  95  88 
92  58  65  79  80 
90  75  74  56  99 
a.  Construct a frequency distribution for this data. Let the first class be 50 – 59 and draw a histogram. 
b.  Construct a cumulative frequency distribution. 
c.  Construct a relative frequency distribution. 
d.  Construct a cumulative relative frequency distribution. 
ANS:
a.  b.  c.  d.  
Cumulative  
Cumulative  Relative  Relative  
Score  Frequency  Frequency  Frequency  Frequency 
50 – 59  3  3  0.15  0.15 
60 – 69  2  5  0.10  0.25 
70 – 79  5  10  0.25  0.50 
80 – 89  4  14  0.20  0.70 
90 – 99  6  20  0.30  1.00 
Total  20  1.00 
PTS: 1 TOP: Descriptive Statistics
 The frequency distribution below was constructed from data collected from a group of 25 students.
Height
(in Inches) 
Frequency 
58 – 63  3 
64 – 69  5 
70 – 75  2 
76 – 81  6 
82 – 87  4 
88 – 93  3 
94 – 99  2 
a.  Construct a relative frequency distribution. 
b.  Construct a cumulative frequency distribution. 
c.  Construct a cumulative relative frequency distribution. 
ANS:
a.  b.  c.  
Cumulative  
Height  Relative  Cumulative  Relative  
(In Inches)  Frequency  Frequency  Frequency  Frequency 
58 – 63  3  0.12  3  0.12 
64 – 69  5  0.20  8  0.32 
70 – 75  2  0.08  10  0.40 
76 – 81  6  0.24  16  0.64 
82 – 87  4  0.16  20  0.80 
88 – 93  3  0.12  23  0.92 
94 – 99  2  0.08  25  1.00 
1.00 
PTS: 1 TOP: Descriptive Statistics
 The frequency distribution below was constructed from data collected on the quarts of soft drinks consumed per week by 20 students.
Quarts of
Soft Drink 
Frequency 
0 – 3  4 
4 – 7  5 
8 – 11  6 
12 – 15  3 
16 – 19  2 
a.  Construct a relative frequency distribution. 
b.  Construct a cumulative frequency distribution. 
c.  Construct a cumulative relative frequency distribution. 
ANS:
a.  b.  c.  
Cumulative  
Quarts of  Relative  Cumulative  Relative  
Soft Drinks  Frequency  Frequency  Frequency  Frequency 
0 – 4  4  0.20  4  0.20 
4 – 8  5  0.25  9  0.45 
8 – 12  6  0.30  15  0.75 
12 – 16  3  0.15  18  0.90 
16 – 20  2  0.10  20  1.00 
Total  20  1.00 
PTS: 1 TOP: Descriptive Statistics
 The grades of 10 students on their first management test are shown below.
94  61  96  66  92 
68  75  85  84  78 
a.  Construct a frequency distribution. Let the first class be 60 – 69. 
b.  Construct a cumulative frequency distribution. 
c.  Construct a relative frequency distribution. 
ANS:
a.  b.  c.  
Cumulative  Relative  
Class  Frequency  Frequency  Frequency 
60 – 69  3  3  0.3 
70 – 79  2  5  0.2 
80 – 89  2  7  0.2 
90 – 99  3  10  0.3 
Total  10  1.0 
PTS: 1 TOP: Descriptive Statistics
 There are 800 students in the School of Business Administration. There are four majors in the School: Accounting, Finance, Management, and Marketing. The following shows the number of students in each major.
Major  Number of Students 
Accounting  240 
Finance  160 
Management  320 
Marketing  80 
Develop a percent frequency distribution and construct a bar chart and a pie chart.
ANS:
Major  Percent Frequency 
Accounting  30% 
Finance  20% 
Management  40% 
Marketing  10% 
PTS: 1 TOP: Descriptive Statistics
 You are given the following data on the ages of employees at a company. Construct a stemandleaf display.
26  32  28  45  58 
52  44  36  42  27 
41  53  55  48  32 
42  44  40  36  37 
ANS:
2  6  7  8  
3  2  2  6  6  7  
4  0  1  2  2  4  4  5  8 
5  2  3  5  8 
PTS: 1 TOP: Descriptive Statistics
 Construct a stemandleaf display for the following data.
12  52  51  37  47  40  38  26  57  31 
49  43  45  19  36  32  44  48  22  18 
ANS:
1  2  8  9  
2  2  6  
3  1  2  6  7  8  
4  0  3  4  5  7  8  9 
5  1  2  7 
PTS: 1 TOP: Descriptive Statistics
 The SAT scores of a sample of business school students and their genders are shown below.
SAT Scores  
Gender  Less than 20  20 up to 25  25 and more  Total 
Female  24  168  48  240 
Male  40  96  24  160 
Total  64  264  72  400 
a.  How many students scored less than 20? 
b.  How many students were female? 
c.  Of the male students, how many scored 25 or more? 
d.  Compute row percentages and comment on any relationship that may exist between SAT scores and gender of the individuals. 
e.  Compute column percentages. 
ANS:
a.  64  
b.  240  
c.  24  
d.  SAT Scores  
Gender  Less than 20  20 up to 25  25 and more  Total  
Female  10%  70%  20%  100%  
Male  25%  60%  15%  100%  
From the above percentages it can be noted that the largest percentages of both genders’ SAT scores are in the 20 to 25 range. However, 70% of females and only 60% of males have SAT scores in this range. Also it can be noted that 10% of females’ SAT scores are under 20, whereas, 25% of males’ SAT scores fall in this category.  
e.  SAT Scores  
Gender  Less than 20  20 up to 25  25 and more  
Female  37.5%  63.6%  66.7%  
Male  62.5%  36.4%  33.3%  
Total  100%  100%  100% 
PTS: 1 TOP: Descriptive Statistics
 For the following observations, plot a scatter diagram and indicate what kind of relationship (if any) exist between x and y.
x  y 
2  7 
6  19 
3  9 
5  17 
4  11 
ANS:
A positive relationship between x and y appears to exist.
CHAPTER 4—INTRODUCTION TO PROBABILITY
MULTIPLE CHOICE
 Each individual outcome of an experiment is called
a.  the sample space 
b.  a sample point 
c.  an experiment 
d.  an individual 
ANS: B PTS: 1 TOP: Probability Concepts
 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 
ANS: A PTS: 1 TOP: Probability Concepts
 A graphical method of representing the sample points of an experiment is
a.  a frequency polygon 
b.  a histogram 
c.  an ogive 
d.  a tree diagram 
ANS: D PTS: 1 TOP: Probability Concepts
 An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist?
a.  4 
b.  16 
c.  8 
d.  32 
ANS: B PTS: 1 TOP: Probability Concepts
 Any process that generates welldefined outcomes is
a.  an event 
b.  an experiment 
c.  a sample point 
d.  a sample space 
ANS: B PTS: 1 TOP: Probability Concepts
 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.  an event 
ANS: C PTS: 1 TOP: Probability Concepts
 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.  a different out come must occur 
ANS: C PTS: 1 TOP: Probability Concepts
 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 
ANS: D PTS: 1 TOP: Probability Concepts
 The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called
a.  permutation 
b.  combination 
c.  multiple step experiment 
d.  None of these alternatives is correct. 
ANS: B PTS: 1 TOP: Probability Concepts
 The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called
a.  permutation 
b.  combination 
c.  multiple step experiment 
d.  None of these alternatives is correct. 
ANS: A PTS: 1 TOP: Probability Concepts
 From a group of six people, two individuals are to be selected at random. How many possible selections are there?
a.  12 
b.  36 
c.  15 
d.  8 
ANS: C PTS: 1 TOP: Probability Concepts
 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 
ANS: A PTS: 1 TOP: Probability Concepts
 A method of assigning probabilities based upon judgment is referred to as the
a.  relative method 
b.  probability method 
c.  classical method 
d.  subjective method 
ANS: D PTS: 1 TOP: Probability Concepts
 A sample point refers to the
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.  sample space 
ANS: C PTS: 1 TOP: Probability Concepts
 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 these alternatives is correct. 
ANS: D PTS: 1 TOP: Probability Concepts
 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 
ANS: C PTS: 1 TOP: Probability Concepts
 Two events are mutually exclusive
a.  if their intersection is 1 
b.  if they have no sample points in common 
c.  if their intersection is 0.5 
d.  None of these alternatives is correct. 
ANS: B PTS: 1 TOP: Probability Concepts
 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 
ANS: C PTS: 1 TOP: Probability Concepts
 Which of the following statements is always true?
a.  1 P(E_{i}) 1 
b.  P(A) = 1 – P(A^{c}) 
c.  P(A) + P(B) = 1 
d.  åP 1 
ANS: B PTS: 1 TOP: Probability Concepts
 Events that have no sample points in common are
a.  independent events 
b.  posterior events 
c.  mutually exclusive events 
d.  complements 
ANS: C PTS: 1 TOP: Probability Concepts
 Initial estimates of the probabilities of events are known as
a.  sets 
b.  posterior probabilities 
c.  conditional probabilities 
d.  prior probabilities 
ANS: D PTS: 1 TOP: Probability Concepts
 Two events with nonzero probabilities
a.  can be both mutually exclusive and independent 
b.  can not be both mutually exclusive and independent 
c.  are always mutually exclusive 
d.  are always independent 
ANS: B PTS: 1 TOP: Probability Concepts
 Two events, A and B, are mutually exclusive and each have 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 
ANS: C PTS: 1 TOP: Probability Concepts
 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 
ANS: C PTS: 1 TOP: Probability Concepts
 The sum of the probabilities of two complementary events is
a.  Zero 
b.  0.5 
c.  0.57 
d.  1.0 
ANS: D PTS: 1 TOP: Probability Concepts
 Events A and B are mutually exclusive if their joint probability is
a.  larger than 1 
b.  less than zero 
c.  zero 
d.  infinity 
ANS: C PTS: 1 TOP: Probability Concepts
 The set of all possible outcomes of an experiment is
a.  an experiment 
b.  an event 
c.  the population 
d.  the sample space 
ANS: D PTS: 1 TOP: Probability Concepts
 Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?
a.  1/52 
b.  2/52 
c.  3/52 
d.  4/52 
ANS: B PTS: 1 TOP: Probability Concepts
 If a dime is tossed four times and comes up tails all four times, the probability of heads on the fifth trial is
a.  smaller than the probability of tails 
b.  larger than the probability of tails 
c.  1/2 
d.  1/32 
ANS: C PTS: 1 TOP: Probability Concepts
 If a six sided die is tossed two times and “3” shows up both times, the probability of “3” on the third trial is
a.  much larger than any other outcome 
b.  much smaller than any other outcome 
c.  1/6 
d.  1/216 
ANS: C PTS: 1 TOP: Probability Concepts
 If A and B are independent events with P(A) = 0.65 and P(A Ç B) = 0.26, then, P(B) =
a.  0.400 
b.  0.169 
c.  0.390 
d.  0.650 
ANS: A PTS: 1 TOP: Probability Concepts
 If P(A) = 0.4, P(B  A) = 0.35, P(A È B) = 0.69, then P(B) =
a.  0.14 
b.  0.43 
c.  0.75 
d.  0.59 
ANS: B PTS: 1 TOP: Probability Concepts
 Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there?
a.  20 
b.  7 
c.  5! 
d.  10 
ANS: D PTS: 1 TOP: Probability Concepts
 Given that event E has a probability of 0.31, 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.  0.69 
d.  is 0.31 
ANS: C PTS: 1 TOP: Probability Concepts
 Three applications for admission to a local university are checked, and it is determined whether each applicant is male or female. The number of sample points in this experiment is
a.  2 
b.  4 
c.  6 
d.  8 
ANS: D PTS: 1 TOP: Probability Concepts
 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.  9 
ANS: D PTS: 1 TOP: Probability Concepts
 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
a.  2 
b.  4 
c.  6 
d.  8 
ANS: D PTS: 1 TOP: Probability Concepts
 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 
ANS: A PTS: 1 TOP: Probability Concepts
 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
a.  9 
b.  14 
c.  24 
d.  36 
ANS: C PTS: 1 TOP: Probability Concepts
 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 these alternatives is correct. 
ANS: D PTS: 1 TOP: Probability Concepts
 If two events are independent, then
a.  they must be mutually exclusive 
b.  the sum of their probabilities must be equal to one 
c.  their intersection must be zero 
d.  None of these alternatives is correct. 
ANS: D PTS: 1 TOP: Probability Concepts
 Bayes’ theorem is used to compute
a.  the prior probabilities 
b.  the union of events 
c.  intersection of events 
d.  the posterior probabilities 
ANS: D PTS: 1 TOP: Probability Concepts
 On a December day, the probability of snow is .30. The probability of a “cold” day is .50. The probability of snow and “cold” weather 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 
ANS: C PTS: 1 TOP: Probability Concepts
 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 åP(E_{i}) = 1 
d.  åP(E_{i}) 1 
ANS: C PTS: 1 TOP: Probability Concepts
 The symbol Ç shows the
a.  union of events 
b.  intersection of two events 
c.  sum of the probabilities of events 
d.  sample space 
ANS: B PTS: 1 TOP: Probability Concepts
 The symbol È shows the
a.  union of events 
b.  intersection of two events 
c.  sum of the probabilities of events 
d.  sample space 
ANS: A PTS: 1 TOP: Probability Concepts
 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.  conditional events 
ANS: B PTS: 1 TOP: Probability Concepts
 If two events are mutually exclusive, then 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 
ANS: A PTS: 1 TOP: Probability Concepts
 The union of events A and B is the event containing
a.  all the sample points belonging to B or A 
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 
ANS: C PTS: 1 TOP: Probability Concepts
 If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is
a.  zero 
b.  1/16 
c.  1/2 
d.  larger than the probability of tails 
ANS: C PTS: 1 TOP: Probability Concepts
 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 
ANS: D PTS: 1 TOP: Probability Concepts
 The union of two events with nonzero probabilities
a.  cannot be less than one 
b.  cannot be one 
c.  could be larger than one 
d.  None of these alternatives is correct. 
ANS: D PTS: 1 TOP: Probability Concepts
 If P(A) = 0.5 and P(B) = 0.5, then P(A Ç B)
a.  is 0.00 
b.  is 1.00 
c.  is 0.5 
d.  None of these alternatives is correct. 
ANS: D PTS: 1 TOP: Probability Concepts
 If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A Ç B) =
a.  0.76 
b.  1.00 
c.  0.24 
d.  0.20 
ANS: C PTS: 1 TOP: Probability Concepts
 If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A È B) =
a.  0.62 
b.  0.12 
c.  0.60 
d.  0.68 
ANS: D PTS: 1 TOP: Probability Concepts
 If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A ½ B) =
a.  0.05 
b.  0.0325 
c.  0.65 
d.  0.8 
ANS: A PTS: 1 TOP: Probability Concepts
 If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A Ç B) =
a.  0.30 
b.  0.15 
c.  0.00 
d.  0.20 
ANS: C PTS: 1 TOP: Probability Concepts
 If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A È B) =
a.  0.00 
b.  0.15 
c.  0.8 
d.  0.2 
ANS: C PTS: 1 TOP: Probability Concepts
 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 
ANS: D PTS: 1 TOP: Probability Concepts
 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 
ANS: B PTS: 1 TOP: Probability Concepts
 Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.2. Then, P(B^{c}) =
a.  0.00 
b.  0.06 
c.  0.7 
d.  0.8 
ANS: D PTS: 1 TOP: Probability Concepts
 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 
ANS: C PTS: 1 TOP: Probability Concepts
 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 È B) = P(A)P(B) 
c.  P(A È B) = P(A) + P(B) 
d.  P(A Ç B) = P(A) + P(B) 
ANS: C PTS: 1 TOP: Probability Concepts
 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 
ANS: D PTS: 1 TOP: Probability Concepts
 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 
ANS: B PTS: 1 TOP: Probability Concepts
 A perfectly balanced coin is tossed 6 times and tails appears on all six tosses. Then, on the seventh trial
a.  tails can not appear 
b.  heads has a larger chance of appearing than tails 
c.  tails has a better chance of appearing than heads 
d.  None of these alternatives is correct. 
ANS: D PTS: 1 TOP: Probability Concepts
 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 
ANS: A PTS: 1 TOP: Probability Concepts
 The set of all possible sample points (experimental outcomes) is called
a.  a sample 
b.  an event 
c.  the sample space 
d.  a population 
ANS: C PTS: 1 TOP: Probability Concepts
 A method of assigning probabilities which assumes that the experimental outcomes are equally likely is referred to as the
a.  objective method 
b.  classical method 
c.  subjective method 
d.  experimental method 
ANS: B PTS: 1 TOP: Probability Concepts
 A method of assigning probabilities based on historical data is called the
a.  classical method 
b.  subjective method 
c.  relative frequency method 
d.  historical method 
ANS: C PTS: 1 TOP: Probability Concepts
 The probability assigned to each experimental outcome must be
a.  any value larger than zero 
b.  smaller than zero 
c.  at least one 
d.  between zero and one 
ANS: D PTS: 1 TOP: Probability Concepts
 If P(A) = 0.58, P(B) = 0.44, and P(A Ç B) = 0.25, then P(A È B) =
a.  1.02 
b.  0.77 
c.  0.11 
d.  0.39 
ANS: B PTS: 1 TOP: Probability Concepts
 If P(A) = 0.50, P(B) = 0.60, and P(A Ç 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 
ANS: C PTS: 1 TOP: Probability Concepts
 If P(A) = 0.62, P(B) = 0.47, and P(A È B) = 0.88, then P(A Ç B) =
a.  0.2914 
b.  1.9700 
c.  0.6700 
d.  0.2100 
ANS: D PTS: 1 TOP: Probability Concepts
 If P(A) = 0.68, P(A È B) = 0.91, and P(A Ç B) = 0.35, then P(B) =
a.  0.22 
b.  0.09 
c.  0.65 
d.  0.58 
ANS: D PTS: 1 TOP: Probability Concepts
 If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then P(A È B) =
a.  0.65 
b.  0.55 
c.  0.10 
d.  0.75 
ANS: B PTS: 1 TOP: Probability Concepts
 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.  1/2 
ANS: D PTS: 1 TOP: Probability Concepts
 If P(A) = 0.50, P(B) = 0.40, then, and P(A È B) = 0.88, then P(B ½ A) =
a.  0.02 
b.  0.03 
c.  0.04 
d.  0.05 
ANS: C PTS: 1 TOP: Probability Concepts
 If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then P(A ½ B) =
a.  0.209 
b.  0.000 
c.  0.550 
d.  0.38 
ANS: D PTS: 1 TOP: Probability Concepts
 If X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then P(X ½ Y) =
a.  0.0944 
b.  0.6150 
c.  1.0000 
d.  0.0000 
ANS: D PTS: 1 TOP: Probability Concepts
 If a six sided die is tossed two times, the probability of obtaining two “4s” in a row is
a.  1/6 
b.  1/36 
c.  1/96 
d.  1/216 
ANS: B PTS: 1 TOP: Probability Concepts
 If A and B are independent events with P(A) = 0.35 and P(B) = 0.20, then, P(A È B) =
a.  0.07 
b.  0.62 
c.  0.55 
d.  0.48 
ANS: D PTS: 1 TOP: Probability Concepts
 If P(A) = 0.7, P(B) = 0.6, P(A Ç B) = 0, then events A and B are
a.  not mutually exclusive 
b.  mutually exclusive 
c.  independent events 
d.  complements of each other 
ANS: B PTS: 1 TOP: Probability Concepts
 If P(A) = 0.45, P(B) = 0.55, and P(A È B) = 0.78, then P(A ½ B) =
a.  zero 
b.  0.45 
c.  0.22 
d.  0.40 
ANS: D PTS: 1 TOP: Probability Concepts
 If P(A) = 0.48, P(A È B) = 0.82, and P(B) = 0.54, then P(A Ç B) =
a.  0.3936 
b.  0.3400 
c.  0.2000 
d.  1.0200 
ANS: C PTS: 1 TOP: Probability Concepts
 Some of the CDs produced by a manufacturer are defective. From the production line, 5 CDs are selected and inspected. How many sample points exist in this experiment?
a.  10 
b.  25 
c.  30 
d.  32 
ANS: D PTS: 1 TOP: Probability Concepts
 An experiment consists of selecting a student body president, vice president, and a treasurer. All undergraduate students, freshmen through seniors, are eligible for the offices. How many sample points (possible outcomes as to the classifications) exist?
a.  12 
b.  16 
c.  64 
d.  100 
ANS: C PTS: 1 TOP: Probability Concepts
 Six applications for admission to a local university are checked, and it is determined whether each applicant is male or female. How many sample points exist in the above experiment?
a.  64 
b.  32 
c.  16 
d.  4 
ANS: A PTS: 1 TOP: Probability Concepts
 Assume your favorite football team has 3 games left to finish the season. The outcome of each game can be win, lose, or tie. How many possible outcomes exist?
a.  7 
b.  27 
c.  36 
d.  64 
ANS: B PTS: 1 TOP: Probability Concepts
 Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or nonpurchaser.)
a.  2 
b.  4 
c.  12 
d.  16 
ANS: D PTS: 1 TOP: Probability Concepts
 From nine cards numbered 1 through 9, two cards are drawn. Consider the selection and classification of the cards as odd or even as an experiment. How many sample points are there for this experiment?
a.  2 
b.  3 
c.  4 
d.  9 
ANS: C PTS: 1 TOP: Probability Concepts
PROBLEM
 A college plans to interview 8 students for possible offer of graduate assistantships. The college has three assistantships available. How many groups of three can the college select?
ANS:
56
PTS: 1 TOP: Probability Concepts
 A student has to take 9 more courses before he can graduate. If none of the courses are prerequisite to others, how many groups of four courses can he select for the next semester?
ANS:
126
PTS: 1 TOP: Probability Concepts
 From among 8 students how many committees consisting of 3 students can be selected?
ANS:
56
PTS: 1 TOP: Probability Concepts
 From a group of seven finalists to a contest, three individuals are to be selected for the first and second and third places. Determine the number of possible selections.
ANS:
210
PTS: 1 TOP: Probability Concepts
 Ten individuals are candidates for positions of president, vice president of an organization. How many possibilities of selections exist?
ANS:
90
PTS: 1 TOP: Probability Concepts
 Assume you have applied for two jobs A and B. The probability that you get an offer for job A is 0.23. The probability of being offered job B is 0.19. The probability of getting at least one of the jobs is 0.38.
a.  What is the probability that you will be offered both jobs? 
b.  Are events A and B mutually exclusive? Why or why not? Explain. 
ANS:
a.  0.04 
b.  No, because P(A Ç B) ¹ 0 
PTS: 1 TOP: Probability Concepts
 Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.
a.  What is the probability that you will receive a Merit scholarship? 
b.  Are events A and M mutually exclusive? Why or why not? Explain. 
c.  Are the two events A, and M, independent? Explain, using probabilities. 
d.  What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship? 
e.  What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship? 
ANS:
a.  0.23 
b.  No, because P(A Ç M) ¹ 0 
c.  No, because P(A Ç M) ¹ P(A) P(M) 
d.  0.4783 
e.  0.6111 
PTS: 1 TOP: Probability Concepts
 A survey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major.
Selected Major
Gender  Management  Marketing  Others  Total 
Male

40  10  30  80 
Female

30  20  70  120 
Total  70  30  100  200 
a.  What is the probability of selecting an individual who is majoring in Marketing? 
b.  What is the probability of selecting an individual who is majoring in Management, given that the person is female? 
c.  Given that a person is male, what is the probability that he is majoring in Management? 
d.  What is the probability of selecting a male individual? 
ANS:
a.  0.15 
b.  0.25 
c.  0.50 
d.  0.40 
PTS: 1 TOP: Probability Concepts
 Sixty percent of the student body at UTC is from the state of Tennessee (T), 30% percent are from other states (O), and the remainder are international students (I). Twenty percent of students from Tennessee live in the dormitories, whereas, 50% of students from other states live in the dormitories. Finally, 80% of the international students live in the dormitories.
a.  What percentage of UTC students live in the dormitories? 
b.  Given that a student lives in the dormitory, what is the probability that she/he is an international student? 
c.  Given that a student lives in the dormitory, what is the probability that she/he is from Tennessee? 
ANS:
a.  35% 
b.  0.2286 (rounded) 
c.  0.3429 (rounded) 
PTS: 1 TOP: Probability Concepts
 The probability of an economic decline in the year 2008 is 0.23. There is a probability of 0.64 that we will elect a republican president in the year 2008. If we elect a republican president, there is a 0.35 probability of an economic decline. Let “D” represent the event of an economic decline, and “R” represent the event of election of a Republican president.
a.  Are “R” and “D” independent events? 
b.  What is the probability of a Republican president and economic decline in the year 2008? 
c.  If we experience an economic decline in the year 2008, what is the probability that there will a Republican president? 
d.  What is the probability of economic decline or a Republican president in the year 2008? Hint: You want to find P(D È R). 
ANS:
a.  No, because P(D) ¹ P(D ½ R) 
b.  0.224 
c.  0.9739 
d.  0.646 
PTS: 1 TOP: Probability Concepts
 As a company manager for Claimstat Corporation there is a 0.40 probability that you will be promoted this year. There is a 0.72 probability that you will get a promotion, a raise, or both. The probability of getting a promotion and a raise is 0.25.
a.  If you get a promotion, what is the probability that you will also get a raise? 
b.  What is the probability that you will get a raise? 
c.  Are getting a raise and being promoted independent events? Explain using probabilities. 
d.  Are these two events mutually exclusive? Explain using probabilities. 
ANS:
a.  0.625 
b.  0.57 
c.  No, because P(R) ¹ P(R ½ P) 
d.  No, because P(R Ç P) ¹ 0 
PTS: 1 TOP: Probability Concepts
 A company plans to interview 10 recent graduates for possible employment. The company has three positions open. How many groups of three can the company select?
ANS:
120
PTS: 1 TOP: Probability Concepts
 A student has to take 7 more courses before she can graduate. If none of the courses are prerequisites to others, how many groups of three courses can she select for the next semester?
ANS:
35
PTS: 1 TOP: Probability Concepts
 How many committees, consisting of 3 female and 5 male students, can be selected from a group of 5 female and 8 male students?
ANS:
560
PTS: 1 TOP: Probability Concepts
 Six vitamin and three sugar tablets identical in appearance are in a box. One tablet is taken at random and given to Person A. A tablet is then selected and given to Person B. What is the probability that
a.  Person A was given a vitamin tablet? 
b.  Person B was given a sugar tablet given that Person A was given a vitamin tablet? 
c.  neither was given vitamin tablets? 
d.  both were given vitamin tablets? 
e.  exactly one person was given a vitamin tablet? 
f.  Person A was given a sugar tablet and Person B was given a vitamin tablet? 
g.  Person A was given a vitamin tablet and Person B was given a sugar tablet? 
ANS:
a.  6/9 
b.  3/8 
c.  1/12 
d.  5/12 
e.  1/2 
f.  1/4 
g.  1/4 
PTS: 1 TOP: Probability Concepts
 The sales records of a real estate agency show the following sales over the past 200 days:
Number of  Number 
Houses Sold  of Days 
0  60 
1  80 
2  40 
3  16 
4  4 
a.  How many sample points are there? 
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