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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
1) The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and the
slips are placed into a hat. If the slips are drawn randomly without replacement, what is
the probability that "A" is drawn first and "B" is drawn second?
A) 0.028
B) 0.033
C) 0.024
D) 0.039
Solve the problem. Round your answer, as needed.
2) There is a huge pile of buttons in which 29% are black, 11% are blue, 17% are orange, 24% are
white, and the rest are clear. You close your eyes, choose a button at random, write down what
color it is, and then put it back in the pile. What is the probability that the third button you choose
is the first one thatʹs clear?
A) 0.007
B) 0.125
C) 0.531
D) 0.157
E) 0.029
3) A manufacturing process has a 77% yield, meaning that 77% of the products are acceptable and
1)
2)
3)
23% are defective. If three of the products are randomly selected, find the probability that all of
them are acceptable.
A) 0.593
B) 0.457
C) 0.231
D) 2.31
E) 0.012
4) You roll a fair die three times. What is the probability that you roll at least one 2?
A) 0.005
B) 0.167
C) 0.5
D) 0.421
4)
E)
0.579
Find the indicated probability.
5) You draw a card at random from a standard deck of 52 cards. Find the probability that the card is
a spade given that it is not a diamond.
A) 0
B) 0.333
C) 0.077
D) 0.5
E) 0.25
6) The table below describes the smoking habits of a group of asthma sufferers.
5)
6)
Light Heavy
Nonsmoker smoker smoker Total
Men
395
63
79
537
Women
363
86
67
516
Total
758
149
146 1053
What is the probability that a woman is a nonsmoker?
A) 0.703
B) 0.720
C) 0.345
D) 0.49
E) 0.479
7) You draw a card at random from a standard deck of 52 cards. Find the probability that the card is
a face card given that it is a king.
A) 0.333
B) 0.077
C) 0.231
1
D) 0.25
E) 1
7)
8) You draw a card at random from a standard deck of 52 cards. Find the probability that the card is
a heart given that it is black.
A) 0.333
B) 0.077
C) 0
D) 0.25
E) 0.5
9) You draw a card at random from a standard deck of 52 cards. Find the probability that the card is
a diamond given that it is a queen.
A) 0.5
B) 0.25
C) 0.333
D) 0.077
8)
9)
E) 0
10) A box contains 16 batteries of which 7 are still working. Anne starts picking batteries one at a
10)
time from the box and testing them. Find the probability that at least one of the first four works.
A) 0.019
B) 0.931
C) 0.081
D) 0.900
E) 0.069
11) An auto insurance company was interested in investigating accident rates for drivers in different
11)
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.
94
160
280
534
64
52
69
185
22
8
26
56
180
220
375
775
If one of these drivers is selected at random, find the probability that the person has had no
accidents in the last three years or is younger than 25.
A) 0.176
B) 0.921
C) 0.522
D) 0.121
E) 0.800
12) A box contains 12 batteries of which 5 are still working. Anne starts picking batteries one at a
time from the box and testing them. Find the probability that she has to pick 5 batteries in order
to find one that works.
A) 0.017
B) 0.044
C) 6.031
D) 0.013
E) 0.001
2
12)
13) The following contingency table provides a joint frequency distribution for a group of retired
people by career and age at retirement.
12
45
79
46
182
8
47
84
30
169
59
181
296
175
711
Suppose one of these people is selected at random. Compute the probability that the person
selected was an attorney who retired between 61 and 65.
A) 0.434
B) 0.416
C) 0.111
D) 0.267
E) 0.256
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13)
14) The following contingency table provides a joint frequency distribution for a group of retired
people by career and age at retirement.
10
37
92
44
183
9
32
92
45
178
58
158
317
188
721
Find the probability that the person was a secretary or retired before the age of 61.
A) 0.306
B) 0.092
C) 0.546
D) 0.404
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E) 0.455
14)
15) The following contingency table provides a joint frequency distribution for a group of retired
15)
people by career and age at retirement.
12
47
92
33
184
9
32
87
45
173
60
168
312
177
717
Suppose one of these people is selected at random. Compute the probability that the person
selected was a store clerk.
A) 0.084
B) 0.254
C) 0.099
D) 0.300
E) 0.025
16) Compute the mean of the random variable with the given discrete probability distribution 16)
x
0
10
25
30
A) 11.2
P(x)
0.2
0.2
0.4
0.2
B) 18
C) 16.25
D) 126.0
17) A fair coin is tossed four times. What is the probability that the sequence of tosses is
HHTT?
A) 0.038
B) 0.125
C) 0.25
D) 0.0625
17)
18) It is estimated that 45% of households own a riding lawn mower. A sample of 11
households is studied. What is the probability that more than 8 of these own a riding
lawn mower?
A) 0.939
B) 0.0610
C) 0.0022
D) 0.0148
18)
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19) Let A and B be events with P(A) = 0.7, P(B) = 0.5, and P(B|A) = 0.4. Find P(A and B).
A) 0.28
B) 0.35
C) 0.2
D) 0.57
19)
20) Let A and B be events with P(A) = 0.4, P(B) = 0.9, and P(A and B) = 0.32. Are A and B
mutually exclusive?
A) No
B) Yes
20)
21) Determine whether the table represents a discrete probability distribution.
21)
x P(x)
5 0.5
6 0.4
7 0.45
8 -0.35
A) No
B) Yes
22) A fast-food restaurant chain has 623 outlets in the United States. The following table
categorizes them by city population and location and presents the number of outlets in
each category. An outlet is chosen at random from the 623 to test market a new menu.
22)
Region
Population
of city
Under 50,000
50,000 - 500,000
Over 500,000
NE
30
60
72
SE
26
48
125
SW NW
27
19
50
39
79
48
Given that the outlet is located in a city with a population under 50,000, what is the
probability that it is in the Southwest?
A) 0.265
B) 0.255
C) 0.164
D) 0.043
Find the expected value of the random variable.
23) A couple plans to have children until they get a boy, but they agree that they will not have more
than four children even if all are girls. Find the expected number of children they will have.
Assume that boys and girls are equally likely. Round your answer to three decimal places.
A) 1.750
B) 1.625
C) 2.500
D) 1.938
E) 1.875
24) You pick a card from a deck. If you get a face card, you win $10. If you get an ace, you win $25
plus an extra $40 for the ace of hearts. For any other card you win nothing.
Find the expected amount you will win.
A) $5.00
B) $5.77
C) $5.48
D) $4.52
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E) $3.46
23)
24)
Create a probability model for the random variable.
25) You have arranged to go camping for two days in March. You believe that the probability that it
will rain on the first day is 0.3. If it rains on the first day, the probability that it also rains on the
second day is 0.8. If it doesnʹt rain on the first day, the probability that it rains on the second day
is 0.3.
Let the random variable X be the number of rainy days during your camping trip. Find the
probability model for X.
0
1
2
A) Rainy days
P(Rainy days) 0.49 0.06 0.24
0
1
2
B) Rainy days
P(Rainy days) 0.49 0.21 0.24
0
1
2
C) Rainy days
P(Rainy days) 0.49 0.42 0.09
0
1
2
D) Rainy days
P(Rainy days) 0.14 0.62 0.24
0
1
2
E) Rainy days
P(Rainy days) 0.49 0.27 0.24
26) You pick a card from a deck. If you get a face card, you win $15. If you get an ace, you win $30
25)
26)
plus an extra $50 for the ace of hearts. For any other card you win nothing.
Create a probability model for the amount you win at this game.
Amount won
$0 $15 $30 $80
A) P(Amount won) 36 12 3 1
52
52 52 52
Amount won
B)
$0 $15 $30 $80
4
1
36 12
P(Amount won) 52
52
52 52
Amount won
C)
$0 $15 $30 $50
4
4
1
39
P(Amount won) 52
52
52
52
Amount won
D)
$0 $15 $30 $50
12
3
1
36
P(Amount won) 52
52
52
52
Amount won
E)
$0 $15 $30 $80
16
3
1
32
P(Amount won) 52
52
52
52
27) Assume a soldier is selected at random from the Army. Determine whether the events A
and B are independent, mutually exclusive, or neither.
A: The soldier is a corporal.
B: The soldier is a colonel.
A) independent
B) mutually exclusive
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C) neither
27)
28) Determine the indicated probability for a binomial experiment with the given number
of trials n and the given success probability p.
n = 15, p = 0.4, P(12)
A) 0.4000
B) 0.0634
C) 0.0000
D) 0.0016
28)
29) Determine the indicated probability for a binomial experiment with the given number
of trials n and the given success probability p.
n = 12, p = 0.6, P(Fewer than 4)
A) 0.0153
B) 0.0028
C) 0.9847
D) 0.0573
29)
30) Let A and B be events with P(A) = 0.8, P(B) = 0.6. Assume that A and B are
independent. Find P(A and B).
A) 0.8
B) 0.48
C) 0.75
D) 0.6
30)
31) An investor is considering a $15,000 investment in a start-up company. She estimates
that she has probability 0.15 of a $5000 loss, probability 0.15 of a $10,000 loss,
probability 0.15 of a $30,000 profit, and probability 0.55 of breaking even (a profit of
$0). What is the expected value of the profit?
A) $10,500
B) $6750
C) $5000
D) $2250
31)
32) Determine whether the table represents a discrete probability distribution.
32)
x P(x)
3 0.3
4 0.05
5 0.45
6 0.2
A) No
B) Yes
33) Let A and B be events with P(A) = 0.9, P(B) = 0.5, and P(A and B) = 0.45. Are A and B
independent?
A) No
B) Yes
33)
34) An unfair coin has a probability 0.4 of landing heads. The coin is tossed two times.
What is the probability that it lands heads at least once?
A) 0.64
B) 0.84
C) 0.6
D) 0.5
34)
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35) It is estimated that 45% of households own a riding lawn mower. A sample of 17
households is studied. What is the probability that no more than 3 of these own a riding
lawn mower?
A) 0.9959
B) 0.9816
C) 0.0184
D) 0.0041
35)
36) An investor is considering a $10,000 investment in a start-up company. She estimates
that she has probability 0.15 of a $5000 loss, probability 0.1 of a $15,000 profit,
probability 0.2 of a $15,000 profit, and probability 0.55 of breaking even (a profit of
$0). What is the expected value of the profit?
A) $5250
B) $8333
C) $9250
D) $3750
36)
37) The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is
estimated that 40% of adult Australian sheep dogs weigh 65 pounds or more. A sample
of 13 adult dogs is studied. What is the probability that exactly 9 of them weigh 65 lb or
more?
A) 0.9757
B) 0.0243
C) 0.1845
D) 0.8155
37)
38) Fill in the missing value so that the following table represents a probability distribution.
38)
x
-2
-1 0 1
P(x) 0.05 0.47 ? 0.32
A) 0.25
B) 0.02
C) 0.07
D) 0.16
39) Let A and B be events with P(A) = 0.2, P(B) = 0.5, and P(A and B) = 0.08. Are A and B
independent?
A) No
B) Yes
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39)
Answer Key
Testname: UNTITLED1
1) B
2) B
3) B
4) D
5) B
6) A
7) E
8) C
9) B
10) B
11) E
12) B
13) C
14) E
15) B
16) B
17) D
18) D
19) A
20) A
21) A
22) A
23) E
24) A
25) E
26) A
27) B
28) D
29) A
30) B
31) D
32) B
33) B
34) A
35) C
36) D
37) B
38) D
39) A
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