Solve the problem.
53)
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?
53)
A)
0.32
B)
0.7
C)
0.58
D)
0.68
Use a tree diagram to find the indicated probability.
54)
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?
54)
A)
0.03
B)
0.42
C)
0.028
D)
0.014
Find the probability.
55)
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?
55)
A)
0
B)
0.8
C)
0.12
D)
0.2
List the outcomes of the sample space.
56)
A box contains 10 red cards numbered 1 through 10. List the sample space of picking one card from
the box.
56)
A)
{1, 10}
B)
{10}
C)
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
D)
{100}
Use Bayes’ rule to find the indicated probability.
57)
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)?
57)
A)
P(rock | positive) = 0.405
B)
P(rock | positive) = 0.53
C)
P(rock | positive) = 0.209
D)
P(rock | positive) = 0.385
Find the expected value.
58)
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?
58)
A)
$300,000
B)
$360,000
C)
$60,000
D)
$218,400
List the outcomes of the sample space.
59)
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.
59)
A)
{1, 2, 3, 4, 5, 6}
B)
{6}
C)
{1, 2, 6}
D)
{36}
Find the expected value.
60)
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?
60)
A)
$3.00
B)
$0.75
C)
–$3.00
D)
$2.00
Solve the problem.
61)
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.
61)
A)
1.6%
B)
2.6%
C)
4.1%
D)
4.0%
Use the tree diagram to find the requested probability.
62)
Find P(MQ). Give your answer as a fraction.
a =0.3, b =0.7, c =0.3, d =0.6, e =0.1, f =0.2, g =0.5, h =0.3
62)
A)
53
100
B)
1
2
C)
35
53
D)
7
20
Use Bayes’ rule to find the indicated probability.
63)
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?
63)
A)
0.385
B)
0.615
C)
0.55
D)
0.45
Find the probability.
64)
A study conducted at a certain college shows that 58% of the school’s graduates find a job in their
chosen field within a year after graduation. Find the probability that among 5 randomly selected
graduates, at least one finds a job in his or her chosen field within a year of graduating.
64)
A)
0.580
B)
0.987
C)
0.934
D)
0.200
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
65)
Find the probability of a house having fewer than 2 DVDs.
65)
A)
0.29
B)
0.38
C)
0.71
D)
0.57
Find the probability.
66)
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)?
66)
A)
P(green apple) =3
5
B)
P(green apple) =1
15
C)
P(green apple) =1
5
D)
P(green apple) = 0
Find the odds.
67)
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.
67)
A)
360:369
B)
39:1
C)
40:1
D)
1:39
Solve the problem.
68)
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)?
68)
A)
0.975
B)
0.05
C)
0.95
D)
0.025
Find the probability.
69)
In a batch of 8,000 clock radios 4% are defective. A sample of 7 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?
69)
A)
0.0400
B)
0.249
C)
0.751
D)
0.143
Find the expected value.
70)
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?
70)
A)
20
B)
100
C)
10
D)
500
Use Bayes’ rule to find the indicated probability.
71)
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?
71)
A)
0.35
B)
0.559
C)
0.224
D)
0.217
Find the odds.
72)
The probability of a person getting a job interview is 0.54. What are the odds against getting the
interview?
72)
A)
1:54
B)
23:27
C)
23:54
D)
54:100
Solve the problem.
73)
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?
73)
A)
0.232
B)
0.303
C)
0.682
D)
0.768
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.
74)
Find the probability that the student is male, P(M).
74)
A)
P(M) =724
1009
B)
P(M) =285
1009
C)
P(M) =424
526
D)
P(M) =171
724
Use Bayes’ rule to find the indicated probability.
75)
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?
75)
A)
0.333
B)
0.5
C)
0.286
D)
0.714
Find the probability.
76)
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)?
76)
A)
P(not green apple) =3
15
B)
P(not green apple) = 0
C)
P(not green apple) =4
5
D)
P(not green apple) =4
15
Use Bayes’ rule to find the indicated probability.
77)
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?
77)
A)
0.275
B)
0.22
C)
0.5667
D)
0.7083
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.
78)
Find the probability that the student is female, given that the student is receiving an education
degree, P(F|E).
78)
A)
P(F|E) =724
1009
B)
P(F|E) =570
2018
C)
P(F|E) =324
666
D)
P(F|E) =51
263
Find the probability.
79)
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)?
79)
A)
4
19
B)
4
17
C)
30
19
D)
4
51
Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the
probability.
80)
Three coins are tossed, and the number of heads is noted.
80)
A)
x P
0 1/6
1 1/3
2 1/3
3 1/6
B)
x P
0 3/16
1 5/16
2 5/16
3 3/16
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
Find the probability.
81)
Find the probability of correctly answering the first 2 questions on a multiple choice test if random
guesses are made and each question has 3 possible answers.
81)
A)
3
2
B)
2
3
C)
1
8
D)
1
9
82)
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?
82)
A)
1
6
B)
1
12
C)
6
D)
1
4
83)
A lottery game has balls numbered 1 through 17. A randomly selected ball has an even number or a
10.
83)
A)
8
B)
5
17
C)
17
5
D)
8
17
84)
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.
84)
A)
0.511
B)
0.471
C)
0.512
D)
0.552
Use Bayes’ rule to find the indicated probability.
85)
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?
85)
A)
0.487
B)
0.856
C)
0.91
D)
0.438
Find the probability.
86)
A sample of 4 different calculators is randomly selected from a group containing 14 that are
defective and 27 that have no defects. What is the probability that at least one of the calculators is
defective?
86)
A)
0.140
B)
0.827
C)
0.812
D)
0.173
Provide an appropriate response.
87)
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
87)
A)
0.35
B)
0.15
C)
0.65
D)
0.20
Find the probability.
88)
A bag contains 6 red marbles, 3 blue marbles, and 1 green marble. What is the probability of
choosing a marble that is not blue?
88)
A)
3
10
B)
10
7
C)
7
10
D)
7
Use Bayes’ rule to find the indicated probability.
89)
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)?
89)
A)
P(clay | positive) = 0.209
B)
P(clay | positive) = 0.53
C)
P(clay | positive) = 0.385
D)
P(clay | positive) = 0.405
Find the probability.
90)
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).
90)
A)
0.840
B)
0.107
C)
0.818
D)
0.182
Provide an appropriate response.
91)
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?
91)
A)
0.62
B)
0.26
C)
0.50
D)
0.22
Answer Key
Testname: C8
Answer Key
Testname: C8
Answer Key
Testname: C8