108)
An auto insurance company was interested in investigating accident rates for drivers in different
age groups. The following contingency table was based on a random sample of drivers and
classifies drivers by age group and number of accidents in the past three years.
95 160 288 543
70 50 62 182
15 10 25 50
180 220 375 775
108)
A)
0.528 0.727 0.768 0.701
0.389 0.227 0.165 0.235
0.083 0.045 0.067 0.065
1.000 1.000 1.000 1.000
B)
0.175 0.295 0.530 1.000
0.385 0.275 0.341 1.000
0.300 0.200 0.500 1.000
0.232 0.284 0.484 1.000
C)
0.123 0.206 0.372 0.701
0.090 0.065 0.080 0.235
0.019 0.013 0.032 0.065
0.232 0.284 0.484 1.000
D)
0.123 0.206 0.372 1.000
0.090 0.065 0.080 1.000
0.019 0.013 0.032 1.000
1.000 1.000 1.000 1.000
109)
In a certain class of students, there are 8 boys from Wilmette, 5 girls from Kenilworth, 10 girls from
Wilmette, 4 boys from Glencoe, 3 boys from Kenilworth and 8 girls from Glencoe. If the teacher
calls upon a student to answer a question, what is the probability that the student will be from
Kenilworth?
109)
A)
0.2
B)
0.211
C)
0.32
D)
0.132
110)
A contingency table provides a joint frequency distribution for the popular votes cast in a
presidential election by sex and political party. A joint probability distribution corresponding to the
contingency table is obtained and can be represented as follows.
The letters a through
are used to represent the probabilities in the different cells so, for example,
the letter f represents P( P2 & S2) and the letter h represents P( S2).
True or false, d + h = 1?
110)
A)
True
B)
False
111)
The table below describes the smoking habits of a group of asthma sufferers.
Nonsmoker
Light
smoker
Heavy
smoker Total
Men 369 70 83 522
Women 381 84 72 537
Total 750 154 155 1059
If one of the 1059 subjects is randomly selected, find the probability that the person chosen is a
woman given that the person is a light smoker.
111)
A)
0.545
B)
0.145
C)
0.156
D)
0.079
112)
In one large city, 73% of adults have health insurance. What is the probability that 6 adults selected
at random from the town all have health insurance?
112)
A)
0.73
B)
0.151
C)
4.38
D)
0.082
113)
If a computer randomly generates 4 digits, what is the probability it will produce a sequence of 4
nines?
113)
A)
1
36
B)
1
40
C)
1
7
D)
1
10,000
114)
A survey conducted in one U.S. city together with information from the census bureau yielded the
following table. The first two columns give a percentage distribution of adults in the city by ethnic
group. The third column gives the percentage of people in each ethnic group who have health
insurance.
Ethnic Group Percentage Percentage with
of adults health insurance
Caucasian 53.9 80
African American 11.6 40
Hispanic 19.8 60
Asian 14.1 69
Other 199.4 55
An adult is selected at random from the city. Determine the probability that the adult obtained is
Asian given that he or she has health insurance.
114)
A)
0.097
B)
0.69
C)
0.001
D)
0.141
115)
The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 4946
21–25 4808
26–30 2673
31–35 2036
36–40 612
Over 40 425
A student from the community college is selected at random. The events A and B are defined as
follows.
A = event the student is between 21 and 40 inclusive
B = event the student is over 25
Describe the event (A or B) in words.
115)
A)
The event the student is between 24 and 25 inclusive
B)
The event the student is between 25 and 40 inclusive
C)
The event the student is 21 or over
D)
The event the student is between 21 and 25 inclusive
C
C
116)
Suppose bivariate data are to be grouped into a contingency table. How many data cells will the
table have if the number of possible values for the two tables are p and q?
116)
A)
p + q
B)
p
q
C)
q
p
D)
pq
117)
If two balanced die are rolled, the possible outcomes can be represented as follows.
(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)
(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)
(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)
(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)
(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)
(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)
Determine the probability that the sum of the dice is 3 or 12.
117)
A)
5
36
B)
1
9
C)
1
18
D)
1
12
118)
The number of hours needed by sixth grade students to complete a research project was recorded
with the following results.
Hours Number of students (f)
425
520
623
7 9
810
9 6
10+8
A student is selected at random. The events A and B are defined as follows.
A = the event the student took between 6 and
9 hours inclusive
B = the event the student took at most 7 hours
Determine the number of outcomes that comprise the event (A or B).
118)
A)
48
B)
125
C)
32
D)
93
119)
True or false, when solving a counting problem, the permutations rule should be used when
repetition is allowed while the combinations rule should be used when repetition is not allowed?
119)
A)
True
B)
False
120)
The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 419
21–25 405
26–30 204
31–35 60
Over 35 29
1117
A student from the community college is selected at random. Find the probability that the student
is at least 31. Round approximations to three decimal places.
120)
A)
89
B)
0.080
C)
0.054
D)
0.920
121)
Two cards are drawn from a deck of 52 cards without replacement. True or false, the unconditional
probability that the second card is a heart is the same as the conditional probability that the second
card is a heart given that the first card was a heart?
121)
A)
True
B)
False
122)
The following contingency table provides a joint frequency distribution for the popular votes cast
in the presidential election by region and political party. Data are in thousands, rounded to the
nearest thousand.
A person who voted in the presidential election is selected at random. Compute the probability that
the person selected was in the West and voted Republican.
122)
A)
0.115
B)
0.588
C)
0.196
D)
0.781
123)
There are 8 members on a board of directors. If they must form a subcommittee of 3 members, how
many different subcommittees are possible?
123)
A)
336
B)
56
C)
512
D)
6
124)
The following contingency table provides a joint frequency distribution for a group of retired
people by career and age at retirement.
843 95 34 180
12 37 82 45 176
59 169 310 178 716
Suppose one of these people is selected at random. Compute P( A2 or C3).
124)
A)
0.253
B)
0.063
C)
0.485
D)
0.422
125)
A contingency table provides a joint frequency distribution for the popular votes cast in a
presidential election by sex and political party. A joint probability distribution corresponding to the
contingency table is obtained and can be represented as follows.
The letters a through
are used to represent the probabilities in the different cells so, for example,
the letter f represents P( P2 & S2) and the letter h represents P( S2).
True or false, if a person who voted in this election is selected at random, the events ( P 1 & S2)
and ( P 2 & S1) are mutually exclusive?
125)
A)
True
B)
False
126)
A percentage distribution is given below for the size of families in one U.S. city.
Size Percentage
239.9
324.4
420.1
510.8
63.3
7+1.5
A family is selected at random. Find the probability that the size of the family is 4 or more. Round
results to three decimal places.
126)
A)
0.357
B)
0.844
C)
0.156
D)
0.201
127)
A relative frequency distribution is given below for the size of families in one U.S. city.
Size Relative frequency
20.405
30.233
40.196
50.107
60.039
7+0.020
A family is selected at random. Find the probability that the size of the family is at most 6. Round
approximations to three decimal places.
127)
A)
0.059
B)
0.941
C)
0.039
D)
0.980
128)
The probability that Luis will pass his statistics test is 0.55. Find the probability that he will fail his
statistics test.
128)
A)
0.45
B)
0.28
C)
1.82
D)
1.22
129)
The Book Industry Study Group, Inc., performs sample surveys to obtain information on
characteristics of book readers. A book reader is defined to be one who read one or more books in
the six months prior to the survey; a non–book reader is defined to be one who read newspapers or
magazines but no books in the six months prior to the survey; a nonreader is defined to be one who
did not read a book, newspaper, or magazine in the six months prior to the survey. The following
data were obtained from a random sample of 1429 persons 16 years old and over.
How many cells does this contingency table have?
129)
A)
12
B)
28
C)
20
D)
16
130)
The number of hours needed by sixth grade students to complete a research project was recorded
with the following results.
Hours Number of students (f)
422
521
617
711
810
9 6
10+5
A student is selected at random. The events A and B are defined as follows.
A = the event the student took at most 8 hours
B = the event the student took at least 8 hours
Determine the number of outcomes that comprise the event (A or B).
130)
A)
10
B)
71
C)
92
D)
103
131)
The table below shows the soft drink preferences of people in three age groups.
cola root beer lemon–lime
under 21 years of age 40 25 20
between 21 and 40 35 20 30
over 40 years of age 20 30 35
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and
drinks cola.
131)
A)
4
17
B)
4
51
C)
4
19
D)
None of the above is correct.
B
C
132)
The number of hours needed by sixth grade students to complete a research project was recorded
with the following results.
Hours Number of students (f)
415
511
619
7 6
8 9
916
10 2
A student is selected at random. The event A is defined as follows.
A = the event the student took at most 7 hours
Describe the event (not A) in words.
132)
A)
The event the student did not take 7 hours
B)
The event the student took more than 7 hours
C)
The event the student took at least 7 hours
D)
The event the student took less than 7 hours
133)
A contingency table provides a joint frequency distribution for the popular votes cast in a
presidential election by sex and political party. A joint probability distribution corresponding to the
contingency table is obtained and can be represented as follows.
The letters a through
are used to represent the probabilities in the different cells so, for example,
the letter f represents P( P2 & S2) and the letter h represents P( S2).
True or false, if a person who voted in this election is selected at random, the events P2 and S2
are mutually exclusive?
133)
A)
True
B)
False
134)
If two cards are drawn without replacement from a deck, find the probability that the second card
is a spade, given that the first card was a spade.
134)
A)
0.216
B)
0.231
C)
0.235
D)
0.917
135)
A company is conducting a sweepstakes, and ships two boxes of game pieces to a particular store.
Box A has 7% of its contents being winners, while 6% of the contents of box B are winners. Box A
contains 40% of the total tickets. If the contents of both boxes are mixed in a drawer and a ticket is
chosen at random, what is the probability it is a winner?
135)
A)
0.13
B)
0.028
C)
0.065
D)
0.064
136)
Sammy and Sally each carry a bag containing a banana, a chocolate bar, and a licorice stick.
Simultaneously, they take out a single food item and consume it. The possible pairs of food items
that Sally and Sammy consumed are as follows.
chocolate bar – chocolate bar
licorice stick – chocolate bar
banana – banana
chocolate bar – licorice stick
licorice stick – licorice stick
chocolate bar – banana
banana – licorice stick
licorice stick – banana
banana – chocolate bar
Find the probability that at least one chocolate bar was eaten.
136)
A)
1
3
B)
7
9
C)
4
5
D)
5
9
137)
A spinner has regions numbered 1 through 21. What is the probability that the spinner will stop on
an even number or a multiple of 3?
137)
A)
17
B)
1
3
C)
2
3
D)
10
9
138)
In a competition, two people will be selected from four finalists to receive the first and second
prizes. The prize winners will be selected by drawing names from a hat. The names of the four
finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows.
JG JH JM GJ GH GM
HJ HG HM MJ MG MH
Here, for example, JG represents the outcome that Jim receives the first prize and George receives
the second prize. List the outcomes that comprise the following event.
A = event that both prize winners are women
138)
A)
HM
B)
HM, MH, HG, MG
C)
HM, MH
D)
HJ, HM, MH
139)
The following frequency distribution analyzes the scores on a math test. Find the probability that a
score greater than 82 was achieved.
139)
A)
0.625
B)
0.813
C)
0.375
D)
0.188
140)
In one large city, 37% of all voters are Democrats. If two voters are randomly selected for a survey,
find the probability that they are both Democrats.
140)
A)
0.740
B)
0.137
C)
0.133
D)
0.370
141)
In a certain lottery, 6 numbers between 1 and 10 inclusive are drawn. These are the winning
numbers. How many different selections are possible? Assume that the order in which the numbers
are drawn is not important.
141)
A)
1,000,000
B)
210
C)
720
D)
151,200
142)
True or false, if a collection of events is exhaustive, then the events must also be mutually
exclusive?
142)
A)
True
B)
False
143)
A bag contains four chips of different colors, including red, blue, green, and yellow. A chip is
selected at random from the bag and then replaced in the bag. A second chip is then selected at
random. Make a list of the possible outcomes (for example RB represents the outcome red chip
followed by blue chip) and use your list to determine the probability that one blue chip and one
yellow chip are selected.
143)
A)
1
8
B)
1
16
C)
1
2
D)
1
4
144)
True or false, if the events A and B are mutually exclusive and the events B and C are mutually
exclusive, then the collection of events A, B, and C must be mutually exclusive?
144)
A)
True
B)
False
145)
Let A and B be events such that P(A) =7
36 ,P(B) =2
9, and P(A or B) =5
18 .
Determine P(A & B).
145)
A)
5
36
B)
25
36
C)
7
162
D)
5
12
146)
In a blood testing procedure, blood samples from 6 people are combined into one mixture. The
mixture will only test negative if all the individual samples are negative. If the probability that an
individual sample tests positive is 0.09, what is the probability that the mixture will test positive?
146)
A)
0.432
B)
1.00
C)
0.568
D)
0.000000531
147)
A class consists of 31 women and 21 men. If a student is randomly selected, what is the probability
that the student is a woman?
147)
A)
21
52
B)
1
52
C)
31
52
D)
31
21
148)
The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 413
21–24 413
25–28 265
29–32 158
33–36 96
37–40 42
Over 40 96
1483
A student from the community college is selected at random. Find the probability that the student
is under 37 years old. Give your answer as a decimal rounded to three decimal places.
148)
A)
0.907
B)
0.065
C)
0.028
D)
0.093
149)
The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 2890
21–24 2190
25–28 1276
29–32 651
33–36 274
37–40 117
Over 40 185
A student from the community college is selected at random. The events A, B, and C are defined as
follows.
A = event the student is at most 28
B = event the student is at least 33
C = event the student is between 21 and 24 inclusive
Is the collection of events A, B, and C mutually exclusive?
149)
A)
Yes
B)
No