Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the probability.
1)
A bag contains 8 red marbles, 9 blue marbles, and 7 green marbles. What is the probability of choosing a blue
marble?
A)
P(B) =9
17
B)
P(B) =7
24
C)
P(B) =1
3
D)
P(B) =3
8
Answer:
D
2)
A lottery game contains 28 balls numbered 1 through 28. What is the probability of choosing a ball numbered
28, P(28)?
A)
P(28) =1
28
B)
P(28) = 0
C)
P(28) = 1
D)
P(28) = 28
Answer:
A
3)
Two 6–sided dice are rolled. What is the probability the sum of the two numbers on the die will be 5, P(sum of
5)?
A)
P(sum of 5) =8
9
B)
P(sum of 5) =5
6
C)
P(sum of 5) =1
9
D)
P(sum of 5) = 4
Answer:
C
4)
A packet of sour worms contains four strawberry, four lime, two black currant, two orange sour, and three
green apples worms. What is the probability that Dustin will choose a green apple sour worm, P(green apple)?
A)
P(green apple) =1
5
B)
P(green apple) = 0
C)
P(green apple) =1
15
D)
P(green apple) =3
5
Answer:
A
5)
A packet of sour worms contains four strawberry, four lime, two black currant, two orange sour, and three
green apples worms. What is the probability that Dylan will not choose a green apple sour worm, P(not green
apple)?
A)
P(not green apple) =4
15
B)
P(not green apple) = 0
C)
P(not green apple) =3
15
D)
P(not green apple) =4
5
Answer:
D
6)
A 6–sided die is rolled. What is the probability of rolling a number less than 6?
A)
1
B)
5
7
C)
5
6
D)
1
6
Answer:
C
1
7)
A bag contains 7 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing a marble
that is not blue?
A)
5
4
B)
4
5
C)
8
D)
1
5
Answer:
B
8)
A bag contains 15 balls numbered 1 through 15. What is the probability of selecting a ball that has an even
number?
A)
15
7
B)
7
15
C)
2
15
D)
7
Answer:
B
9)
Two 6–sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater
than 9?
A)
1
6
B)
6
C)
1
12
D)
1
4
Answer:
A
10)
A sample space consists of 121 separate events that are equally likely. What is the probability of each?
A)
1
121
B)
121
C)
1
D)
0
Answer:
A
11)
Find the probability of correctly answering the first 5 questions on a multiple choice test if random guesses are
made and each question has 6 possible answers.
A)
1
7776
B)
6
5
C)
1
15625
D)
5
6
Answer:
A
List the outcomes of the sample space.
12)
A 6–sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6. List the sample space of rolling one die.
A)
{1, 2, 3, 4, 5, 6}
B)
{36}
C)
{6}
D)
{1, 2, 6}
Answer:
A
13)
A box contains 10 blue cards numbered 1 through 10. List the sample space of picking one card from the box.
A)
{100}
B)
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C)
{10}
D)
{8}
Answer:
B
14)
A group of 18 songs are assigned numbers 1 through 18. List the outcomes of sample space of the event
choosing a song with a number 5 or less.
A)
{1, 2, 3, 4}
B)
{1, 2, 3, 4, 5}
C)
{18}
D)
{1}
Answer:
B
15)
A box contains 10 red cards numbered 1 through 10. List the sample space of picking one card from the box.
A)
{10}
B)
{100}
C)
{1, 10}
D)
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Answer:
D
2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
16)
A fair die and a fair coin are tossed in succession. Find the sample space composed of equally likely events.
Answer:
{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
17)
There are 3 balls in a hat; one with the number 2 on it, one with the number 6 on it, and one with the number 8
on it. You pick a ball from the hat at random and then you flip a coin. Using a tree diagram , obtain the sample
space for the experiment. List the elements that make up the sample space.
A)
2 H T, 6 H T, 8 H T
B)
2 H, 6 H, 8 H
C)
2 6 8 H, 2 6 8 T
D)
2 H, 2 T, 6 H, 6 T, 8 H, 8 T
Answer:
D
Find the indicated probability.
18)
In a family with family with 4 children, excluding multiple births, what is the probability of having 2 girls and
2 boys, in that order? Assume that a boy is as likely as a girl at each birth.
A)
1
8
B)
1
2
C)
1
16
D)
1
4
Answer:
C
19)
In a homicide case 3 different witnesses picked the same man from a line up. The line up contained 5 men. If the
identifications were made by random guesses, find the probability that all 3 witnesses would pick the same
person.
A)
0.008
B)
0.0041152
C)
0.04
D)
0.6
Answer:
A
Find the probability.
20)
A single fair die is rolled. The number on the die is a 3 or a 5.
A)
1
6
B)
2
C)
1
3
D)
1
36
Answer:
C
21)
A lottery game has balls numbered 1 through 15. A randomly selected ball has an even number or a 4.
A)
7
15
B)
7
C)
3
10
D)
10
3
Answer:
A
22)
At the Stop ‘n Go tune–up and brake shop, the manager has found that an SUV will require a tune–up with a
probability of 0.6, a brake job with a probability of 0.1 and both with a probability of 0.02. What is the
probability that an SUV requires either a tune–up or a brake job?
A)
0.32
B)
0.7
C)
0.58
D)
0.68
Answer:
D
3
23)
The table below describes the smoking habits of a group of asthma sufferers.
Nonsmoker Occasional
smoker Regular
smoker Heavy
smoker Total
Men 363 33 89 46 531
Women 443 40 66 44 593
Total 806 73 155 90 1124
If one of the 1124 people is randomly selected, find the probability that the person is a man or a heavy smoker.
A)
0.511
B)
0.512
C)
0.552
D)
0.471
Answer:
B
24)
Samantha is taking courses in math and English. The probability of passing math is estimated at 0.4 and English
at 0.6. She also estimates that the probability of passing at least one of them is 0.8. What is her probability of
passing both courses?
A)
0
B)
0.12
C)
0.2
D)
0.8
Answer:
C
25)
A study conducted at a certain college shows that 62% of the school’s graduates find a job in their chosen field
within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one
finds a job in his or her chosen field within a year of graduating.
A)
0.143
B)
0.999
C)
0.965
D)
0.620
Answer:
B
26)
A sample of 4 different calculators is randomly selected from a group containing 10 that are defective and 28
that have no defects. What is the probability that at least one of the calculators is defective?
A)
0.100
B)
0.723
C)
0.277
D)
0.705
Answer:
B
27)
In a batch of 8,000 clock radios 6% are defective. A sample of 9 clock radios is randomly selected without
replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective.
What is the probability that the entire batch will be rejected?
A)
0.573
B)
0.111
C)
0.0600
D)
0.427
Answer:
D
Find the odds.
28)
In a certain town, 20% of people commute to work by bus. If a person is selected randomly from the town, what
are the odds against selecting someone who commutes by bus?
A)
1:4
B)
4:1
C)
1:5
D)
4:5
Answer:
B
29)
Suppose you are playing a game of chance. If you bet $9 on a certain event, you will collect $360(including your
$9 bet) if you win. Find the odds used for determining the payoff.
A)
39:1
B)
1:39
C)
360:369
D)
40:1
Answer:
A
30)
If two fair dice are thrown, what are the odds of obtaining a sum of 7?
A)
3:4
B)
1:6
C)
1:5
D)
5:1
Answer:
C
4
31)
The probability of a person getting a job interview is 0.54. What are the odds against getting the interview?
A)
54:100
B)
23:54
C)
1:54
D)
23:27
Answer:
D
32)
If the sectors are of equal size, what are the odds of spinning an A on this spinner?
A)
2:6
B)
3:5
C)
6:2
D)
4:2
Answer:
B
In a survey of the number of DVDs in a house, the table shows the probabilities.
Number of DVDs 0 1 2 3 4 or more
Probability 0.05 0.024 0.33 0.21 0.17
33)
Find the probability of a house having 1 or 2 DVDs.
A)
0.57
B)
0.83
C)
0.95
D)
0.38
Answer:
A
34)
Find the probability of a house having 3 or more DVDs.
A)
0.57
B)
0.83
C)
0.05
D)
0.38
Answer:
D
35)
Find the probability of a house having fewer than 2 DVDs.
A)
0.71
B)
0.29
C)
0.57
D)
0.38
Answer:
B
Estimate the indicated probability.
36)
College students were given three choices of pizza toppings and asked to choose one favorite. The following
table shows the results.
toppings freshman sophomore junior senior
cheese 15 11 23 28
meat 20 28 11 15
veggie 11 15 20 28
A randomly selected student prefers a cheese topping.
A)
.342
B)
.124
C)
.329
D)
.364
Answer:
A
5
37)
College students were given three choices of pizza toppings and asked to choose one favorite. The following
table shows the results.
toppings freshman sophomore junior senior
cheese 10 14 25 28
meat 25 28 14 10
veggie 14 10 25 28
A randomly selected student who is a a junior or senior is also prefers veggie. Round the answer to the nearest
hundredth.
A)
.391
B)
.408
C)
.229
D)
.688
Answer:
B
38)
College students were given three choices of pizza toppings and asked to choose one favorite. The following
table shows the results.
toppings freshman sophomore junior senior
cheese 11 16 27 25
meat 23 25 16 11
veggie 16 11 23 25
A randomly selected student prefers a cheese topping.
A)
.139
B)
.048
C)
.460
D)
.345
Answer:
D
Solve the problem.
39)
Of the coffee makers sold in an appliance store, 4.0% have either a faulty switch or a defective cord, 2.5% have a
faulty switch, and 0.1% have both defects. What is the probability that a coffee maker will have a defective cord?
Express the answer as a percentage.
A)
4.0%
B)
4.1%
C)
2.6%
D)
1.6%
Answer:
D
40)
At the Stop ‘n Go tune–up and brake shop, the manager has found that an SUV will require a tune–up with a
probability of 0.6, a brake job with a probability of 0.1 and both with a probability of 0.02. What is the
probability that an SUV requires neither type of repair?
A)
0.7
B)
0.32
C)
0.68
D)
0.58
Answer:
B
41)
At the Stop ‘n Go tune–up and brake shop, the manager has found that an SUV will require a tune–up with a
probability of 0.6, a brake job with a probability of 0.1 and both with a probability of 0.02. What is the
probability that an SUV requires a tune–up but not a brake job?
A)
0.02
B)
0.58
C)
0.68
D)
0.7
Answer:
B
6
42)
A drug company is running trials on a new test for anabolic steroids. The company uses the test on 400 athletes
know to be suing steroids and 200 athletes known not to be using steroids. Of those using steroids, the new test
is positive for 390 and negative for 10. Of those not using steroids, the test is positive for 10 and negative for 190.
What is the estimated probability of a false negative result (the probability that an athlete using steroids will test
negative)?
A)
0.975
B)
0.05
C)
0.95
D)
0.025
Answer:
D
43)
The distribution of bachelor degrees conferred by a local college is listed below, by major.
Major Frequency
English 2073
Mathematics 2164
Chemistry 318
Physics 856
Liberal Arts 1358
Business 1676
Engineering 868
9313
What is the probability that a randomly selected degree is not in Mathematics?
A)
0.768
B)
0.682
C)
0.303
D)
0.232
Answer:
A
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
44)
Two groups of people were asked their preference in television programs from among three new programs. The results
are shown in the table below. What is the probability that a person selected at random will be from group A or prefer
program X?
Television Program
Group of People X Y Z
A25 15 40
B20 60 50
Answer:
100
210
0.476
45)
From a survey involving 2,000 students at a large university, it was found that 1,300 students had classes on
Monday, Wednesday, and Friday; 1,500 students had classes on Tuesday and Thursday; and 800 students had
classes every day. If a student at this university is selected at random, what is the (empirical) probability that
the student has classes only on Tuesday and Thursday?
Answer:
0.350
7
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
The graduates at a southern university are shown in the table.
Art & Science
A Education
E Business
B Total
Male, M 342 424 682 1448
Female, F 324 102 144 570
Total 666 526 826 2018
A student is selected at random from the graduating class.
46)
Find the probability that the student is male, P(M).
A)
P(M) =285
1009
B)
P(M) =424
526
C)
P(M) =724
1009
D)
P(M) =171
724
Answer:
C
47)
Find the probability that the student is female, given that the student is receiving an education degree, P(F|E).
A)
P(F|E) =570
2018
B)
P(F|E) =324
666
C)
P(F|E) =51
263
D)
P(F|E) =724
1009
Answer:
C
48)
Find the probability that the student is female, given that an education degree is not received, P(F|E’).
A)
P(F|E’) =117
373
B)
P(F|E’) =324
666
C)
P(F|E’) =424
526
D)
P(F|E’) =102
526
Answer:
A
Use a tree diagram to find the indicated probability.
49)
3.9% of a secluded island tribe are infected with a certain disease. There is a test for the disease, however the
test is not completely accurate. 92% of those who have the disease will test positive. However 4.4% of those
who do not have the disease will also test positive (false positives). What is the probability that any given
person will test positive? Round your answer to three decimal places if necessary.
A)
0.482
B)
0.078
C)
0.036
D)
0.042
Answer:
B
50)
In the town of Cheraw, a certain type of laptop computer is sold at just two stores. Store A has 38% of the sales,
4% of which are of defective items, and store B has 62% of the sales, 2% of which are of defective items. A
person receives one of these laptop computers as a gift. What is the probability it is defective?
A)
0.014
B)
0.028
C)
0.42
D)
0.03
Answer:
B
Use the tree diagram to find the requested probability.
51)
Find P(X
A). Give your answer as a decimal and round your answer to three decimal places if necessary.
a =0.1, b =0.9, c =0.8, d =0.2, e =0.3, f =0.7
A)
0.08
B)
0.073
C)
0.229
D)
0.8
Answer:
C
8
Find the probability.
52)
People were given three choices of soft drinks and asked to choose one favorite. The following table shows the
results.
diet cola root beer lemon drop
under 18 years of age 40 25 20
between 18 and 40 35 20 30
over 40 years of age 20 30 35
P(person is over 40
person drinks diet cola)?
A)
4
17
B)
4
51
C)
30
19
D)
4
19
Answer:
B
53)
The table shows the political affiliation of voters in a small midwestern town and their positions on stronger drug control
laws.
Stronger Drug Control
Favor Oppose
Republican 0.11 0.27
Democrat 0.25 0.16
Other 0.15 0.06
Find the probability that a Democrat opposes stronger drug control laws.
A)
0.420
B)
0.390
C)
0.350
D)
0.490
Answer:
B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
54)
A box contains 7 red balls and 3 white balls. Two balls are to be drawn in succession without replacement. What
is the probability that the sample will contain exactly one white ball and one red ball?
Answer:
42
90
0.467
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine independence. Answer Yes or No.
55)
The table shows the political affiliation of voters in one city and their positions on stronger gun control laws.
Stronger Gun Control
Favor Oppose
Republican 0.08 0.33
Democrat 0.22 0.20
Other 0.13 0.04
Are party affiliation and position on gun control laws independent?
A)
Yes
B)
No
Answer:
B
9
56)
According to a survey, 8% of students at a college are left handed, 53% are female, and 4.24% are both female
and left handed. Is being left handed independent of gender?
A)
Yes
B)
No
Answer:
A
57)
A group of 25 people contains 10 brunettes, 8 blondes, and 7 redheads. Of the 20 girls in the group, 8 are
brunettes, 6 are blondes, and 6 are redheads. A person is selected at random. Are the events of being a girl and
having brown hair independent?
A)
Yes
B)
No
Answer:
A
Find the probability.
58)
The table lists the eight possible blood types. Also given is the percent of the U.S. population having that type.
Type/RH factor Percent
O positive 38%
A positive 34%
B Positive 9%
O Negative 7%
A Negative 6%
AB Positive 3%
B Negative 2%
AB Negative 1%
Let E be the event that a randomly selected person in the U. S. has type B blood. Let F be the event that a randomly
selected person in the U. S. has RH–positive blood.
Find P(F|E).
A)
0.818
B)
0.340
C)
0.720
D)
0.107
Answer:
D
59)
The table lists the eight possible blood types. Also given is the percent of the U.S. population having that type.
Type/RH factor Percent
O positive 38%
A positive 34%
B Positive 9%
O Negative 7%
A Negative 6%
AB Positive 3%
B Negative 2%
AB Negative 1%
Let E be the event that a randomly selected person in the U. S. has type B blood. Let F be the event that a randomly
selected person in the U. S. has RH–positive blood.
Find P(E|F).
A)
0.107
B)
0.818
C)
0.182
D)
0.840
Answer:
B
10
60)
People were given three choices of soft drinks and asked to choose one favorite. The following table shows the
results.
diet cola root beer lemon–drop
under 18 years of age 40 25 20
between 18 and 40 35 20 30
over 40 years of age 20 30 35
Find P(person is over 40|person drinks root beer).
A)
5
17
B)
20
17
C)
6
17
D)
2
5
Answer:
D
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
61)
Refer to the table below for events in a sample space, S, compute P(C|E).
A B C Total
D 0.12 0.50 0.08 0.70
E 0.03 0.10 0.17 0.30
Totals 0.15 0.60 0.25 1.00
Answer:
0.5667
62)
A class of 40 students has 10 honor students and 13 athletes. Three of the honor students are also athletes. One
student is chosen at random. Find the probability that this student is an athlete if it is known that the student is
not an honor student.
Answer:
1
3
0.333
63)
Each person in a group of students was identified by his or her hair color and then asked whether he or she preferred
taking classes in the morning, afternoon, or evening. The results are shown in the table below. Find the probability that
a student preferred morning classes given that he or she has blonde hair.
Hair Color
Class Time Preference Blonde Brunette Rehead
Morning 45 25 10
Afternoon 40 15 50
Evening 35 20 30
Answer:
45
120 = 0.375
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
64)
If 82% of scheduled flights actually take place and cancellations are independent events, what is the probability
that 3 separate flights will all take place?
A)
.82
B)
.55
C)
.01
D)
.67
Answer:
B
11
65)
A calculator requires a keystroke assembly and a logic circuit. Assume that 91% of the keystroke assemblies and
93% of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory.
Assume that defects in keystroke assemblies are independent of defects in logic circuits.
A)
.8649
B)
.9200
C)
.8463
D)
.8281
Answer:
C
Use the tree diagram to find the requested probability.
66)
Find P(X
A). Give your answer as a decimal and round your answer to three decimal places if necessary.
a =0.7, b =0.3, c =0.1, d =0.9, e =0.2, f =0.8
A)
0.1
B)
0.233
C)
0.538
D)
0.07
Answer:
C
67)
Find P(M
Q). Give your answer as a fraction.
a =0.2, b =0.8, c =0.7, d =0.2, e =0.1, f =0.3, g =0.1, h =0.6
A)
3
25
B)
2
3
C)
1
10
D)
2
25
Answer:
B
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the probability.
68)
One urn has 4 red balls and 1 white ball; a second urn has 2 red balls and 3 white balls. A single card is
randomly selected from a standard deck. If the card is less than 5 (aces count as 1), a ball is drawn out of the first
urn; otherwise a ball is drawn out of the second urn. If the drawn ball is red, what is the probability that it came
out of the second urn?
Answer:
P(Urn 2 R) =9
17 = 0.5294
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use Bayes’ rule to find the indicated probability.
69)
Two shipments of components were received by a factory and stored in two separate bins. Shipment I has 2% of
its contents defective, while shipment II has 5% of its contents defective. If it is equally likely an employee will
go to either bin and select a component randomly, what is the probability that a defective component came from
shipment II?
A)
0.5
B)
0.333
C)
0.714
D)
0.25
Answer:
C
12
70)
Two stores sell a certain MP3 players. Store A has 34% of the sales, 5% of which are of defective items, and store
B has 66% of the sales, 1% of which are of defective items. The difference in defective rates is due to different
levels of pre–sale checking of the product. A person receives a defective item of this product as a gift. What is
the probability it came from store B?
A)
0.22
B)
0.7083
C)
0.275
D)
0.5667
Answer:
C
71)
The incidence of a certain disease on the island of Tukow is 4%. A new test has been developed to diagnose the
disease. Using this test, 91% of those who have the disease test positive while 4% of those who do not have the
disease test positive (false positive). If a person tests positive, what is the probability that he or she actually has
the disease?
A)
0.438
B)
0.91
C)
0.487
D)
0.856
Answer:
C
72)
Quality Motors has three plants. Plant 1 produces 35% of the car output, plant 2 produces 20% and plant 3
produces the remaining 45%. One percent of the output of plant 1 is defective, 1.8% of the output of plant 2 is
defective and 2% of the output of plant 3 is defective. The annual total production of Quality Motors is 1,000,000
cars. A car chosen at random from the annual output and is found defection. What is the probability that it came
from plant 2?
A)
0.217
B)
0.35
C)
0.559
D)
0.224
Answer:
D
73)
In Cumberland County, 55% of registered voters are Democrats, 30% are Republicans and 15% are independent.
During a recent election, 35% of the Democrats voted, 65% of the Republicans voted, and 75% of the
independent voted. What is the probability that someone who voted is a Democrat?
A)
0.615
B)
0.55
C)
0.45
D)
0.385
Answer:
D
74)
In Cumberland County, 55% of registered voters are Democrats, 30% are Republicans and 15% are independent.
During a recent election, 35% of the Democrats voted, 65% of the Republicans voted, and 75% of the
independent voted. What is the probability that someone who voted is a Republican?
A)
0.225
B)
0.39
C)
0.065
D)
0.385
Answer:
B
75)
An water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock
P(R) = 0.53. The clay probability is P(C) = 0.21. The sand probability is P(S) = 0.26. It if it rock, a geological test
gives a positive result with 35% accuracy. If it is clay, this test gives a positive result with 48% accuracy. The test
gives a 75% accuracy for sand. Given the test is positive, what is the probability that soil is rock, P(rock |
positive)?
A)
P(rock | positive) = 0.209
B)
P(rock | positive) = 0.405
C)
P(rock | positive) = 0.53
D)
P(rock | positive) = 0.385
Answer:
D
76)
An water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock
P(R) = 0.53. The clay probability is P(C) = 0.21. The sand probability is P(S) = 0.26. It if it rock, a geological test
gives a positive result with 35% accuracy. If it is clay, this test gives a positive result with 48% accuracy. The test
gives a 75% accuracy for sand. Given the test is positive, what is the probability that soil is clay, P(clay |
positive)?
A)
P(clay | positive) = 0.53
B)
P(clay | positive) = 0.209
C)
P(clay | positive) = 0.385
D)
P(clay | positive) = 0.405
Answer:
B
13
77)
An water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock
P(R) = 0.53. The clay probability is P(C) = 0.21. The sand probability is P(S) = 0.26. It if it rock, a geological test
gives a positive result with 35% accuracy. If it is clay, this test gives a positive result with 48% accuracy. The test
gives a 75% accuracy for sand. Given the test is positive, what is the probability that soil is rock, P(sand |
positive)?
A)
P(sand | positive) = 0.405
B)
P(sand | positive) = 0.385
C)
P(sand | positive) = 0.26
D)
P(sand | positive) = 0.209
Answer:
A
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the probability.
78)
A basketball team is to play two games in a tournament. The probability of winning the first game is .10. If the
first game is won, the probability of winning the second game is .15. If the first game is lost, the probability of
winning the second game is .25. What is the probability the first game was won if the second game is lost?
Answer:
P( win first game | lose second game) =17
152
0.1118
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the expected value.
79)
Suppose that 1,000 tickets are sold for a raffle that has the following prizes: one $300 prize, two $100 prizes, and
one hundred $1 prizes. What is expected value of a ticket?
A)
$1
B)
$100
C)
$0.60
D)
$300
Answer:
C
80)
A fair coin is tossed three times, and a player wins $3 if 3 tails occur, wins $2 if 2 tails occur and loses $3 if no
tails occur. If one tail occurs, no one wins. What is the expected value of the games?
A)
$2.00
B)
–$3.00
C)
$3.00
D)
$0.75
Answer:
D
81)
A new light bulb has been found to have a 0.02 probability of being defective. A shop owner receives 500 bulbs
of this kind. How many of these bulbs are expected to be defective?
A)
10
B)
100
C)
20
D)
500
Answer:
A
82)
A car agency has found daily demand to be as shown in the table.
Number of customers 7 8 9 10 11
Probability 0.10 0.20 0.40 0.20 0.10
Find the expected number of customers.
A)
2
B)
12
C)
9
D)
10
Answer:
C
14
Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the
probability.
83)
Two marbles are drawn from a bag in which there are 4 red marble and 2 blue marble. The number of blue
marbles is counted.
A)
x P
0 0.07
1 0.53
2 0.4
B)
x P
0 0.719
1 0.280
2 0.001
C)
x P
0 0.333
1 0.333
2 0.333
D)
x P
0 0.4
1 0.53
2 0.07
Answer:
D
84)
Three coins are tossed, and the number of heads is noted.
A)
x P
0 3/16
1 5/16
2 5/16
3 3/16
B)
x P
0 1/6
1 1/3
2 1/3
3 1/6
C)
x P
0 1/3
1 1/6
2 1/6
3 1/3
D)
x P
0 1/8
1 3/8
2 3/8
3 1/8
Answer:
D
Provide an appropriate response.
85)
In a raffle 1000 tickets are being sold at $1.00 each. The first prize is $100, and there are 3 second prizes fo $50
each. By how much does the price of a ticket exceed its expected value?
A)
$1.75
B)
$50
C)
$0.75
D)
$1.00
Answer:
C
86)
The number of loaves of whole wheat bread left on the shelf of a local quick stop at closing (denoted by the random
variable X) varies from day to day. Past records show that the probability distribution of X is as shown in the following
table. Find the probability that there will be at least three loaves left over at the end of any given day.
xi0 1 2 3 4 5 6
pi 0.20 0.25 0.20 0.15 0.10 0.08 0.02
A)
0.15
B)
0.65
C)
0.20
D)
0.35
Answer:
D
87)
The probability distribution for the random variable X is:
xi–1 0 1 2
pi 0.22 0.23 0.26 0.29
What is the expected value of X?
A)
0.62
B)
0.50
C)
0.22
D)
0.26
Answer:
A
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
88)
A shipment of 20 digital cameras contains two that are defective. A random sample of three is selected and
tested. Let X be the random variable associated with the number of defective cameras in a sample. Find the
probability distribution of X and the expected number of defective cameras in a sample.
Answer:
xi0 1 2
pi0.7158 0.2684 0.0158; 0.3
15
89)
The payoff table for three possible courses of action A1, A2, and A3 is given below.
pi
A1
xi
A2
xi
A3
xi
.3 $70 $40 $50
.2 $100 $120 $110
.1 $160 $140 $90
.4 $80 $140 $160
Which course of action will produce the largest expected value? What is it?
Answer:
A3 has the largest expected value. E(A3) = 110
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the expected value.
90)
Mr. Cameron is sponsoring an summer concert. He estimates that he will make $300,000 if it does not rain and
make $60,000 if it does rain. The weather bureau predicts the chance of rain is 0.34 for the day of the concert.
What are Mr. Cameron’s expected concert earning?
A)
$360,000
B)
$60,000
C)
$300,000
D)
$218,400
Answer:
D
91)
Mr. Cameron is sponsoring an summer concert. He estimates that he will make $300,000 if it does not rain and
make $60,000 if it does rain. The weather bureau predicts the chance of rain is 0.34 for the day of the concert. An
insurance company is willing to insure the concert for $150,000 against rain for a premium of $30,000. If he buys
this policy, what are his expected earnings from the concert?
A)
$239,400
B)
$180,000
C)
$300,000
D)
$270,000
Answer:
A
16