5_4
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Draw a tree diagram to represent the problem. At the end of each branch use symbols to represent the event that the
branch corresponds to and give the probability of the event.
1) A bag contains 11 red chips and 8 blue chips. Two chips are selected randomly without
1)
replacement from the bag. Draw a tree diagram showing the possible outcomes and their
probabilities for this problem.
A)
B)
C)
1
D)
E)
2) Two cards are selected randomly without replacement from a standard deck of 52 cards. The color
of each card (red or black) is recorded. Draw a tree diagram showing the possible outcomes and
their probabilities for this problem.
A)
2
2)
B)
C)
D)
3
E)
Provide an appropriate response.
3) The expression P(A and B) = P(A)P(B|A) is valid if
A) for any events A and B.
B) A and B are mutually exclusive.
C) A and B are dependent.
D) A and B are independent.
E) only if A equals B .
4) If A and B are independent events, with P(A) =
A) equals
3)
1
2
, P(B) = , then P(A or B)
5
5
4)
3
.
25
B) cannot be determined from the given information.
13
.
C) equals
25
D) equals
3
.
5
E) equals
3
.
10
5) If A and B are mutually exclusive events with P(A) =
A)
19
.
49
B) 0.
C) 1.
1
2
, P(B) = , then P(A or B) equals
7
7
D)
3
.
7
E)
5)
2
.
47
6) For a particular test, the sensitivity and specificity were reported as 0.96 and 0.93. Suppose the
prevalence rate was actually 0.03. Calculate the probability that the individual actually is a drug
user given that the test result is positive.
A) 0.227
B) 0.10
C) 0.04
D) 0.93
E) 0.07
4
6)
7) The first two columns of the table below give a percentage distribution for adults in one city by
income group. The third column gives the percentage of people in each income group who plan to
buy a new car next year.
Income
(dollars)
0 - 4999
5000 - 9999
10,000 - 14,999
15,000 - 19,999
20,000 - 24,999
25,000 - 29,999
30,000 - 34,999
35,000 - 39,999
40,000 - 49,999
50,000 and over
Percentage
of population
5.2
6.4
5.4
8.7
9.4
10.2
13.8
10.7
15.5
14.7
7)
Percentage that will
buy new car next year
2
3
6
7
9
10
11
13
15
19
An adult is picked at random from the city. Given that the person selected plans to buy a new car
next year, what is the probability that their income is $50,000 or over?
A) 0.22
B) 0.21
C) 0.28
D) 0.24
E) 0.25
Find the indicated probability.
8) The table below shows the careers of a group of retired people and their ages at retirement.
What is the probability that a person who retired between the ages of 56 and 60 was a college
professor?
A) 0.251
B) 0.244
C) 0.060
D) 0.238
E) 0.114
5
8)
9) An automobile insurance company was interested in investigating accident rates for drivers in
different age groups. The following table classifies drivers by age group and accident rate based on
a random sample of drivers.
9)
What is the probability that a person who had no accidents in the past three years is over 45?
A) 0.749
B) 0.535
C) 0.465
D) 0.484
E) 0.363
10) The table below describes the smoking habits of a group of asthma sufferers.
10)
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) 0.479
C) 0.345
D) 0.297
E) 0.490
11) The table below describes the smoking habits of a group of asthma sufferers.
11)
Light Heavy
Nonsmoker smoker smoker Total
Men
331
65
61
457
Women
358
65
86
509
Total
689
130
147
966
What is the probability that a light smoker is a woman?
A) 0.5
B) 0.135
C) 0.67
6
D) 0.44
E) 0.128
Provide an appropriate response.
12) (From Hans Reichenbach's The Theory of Probability, University of California Press, 1949.) Mr.
Smith's gardener is not dependable; the probability that he will forget to water the rosebush during
Smith's absence is 2/3. The rosebush is in questionable condition anyhow; if watered, the
probability of its withering is 1/2, but if it is not watered, the probability of its withering is 3/4.
Upon returning, Smith finds that the rosebush has withered. What is the probability that the
gardener did not water the rosebush?
1
A)
2
B)
12)
1
3
C) None of these.
3
D)
4
E)
2
3
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
13) Photo Max employs 3 film developers. Alice develops 42% of the film, and her customers
are dissatisfied only 1% of the time. Bo develops 38% of the film, and his customers are
dissatisfied only 2% of the time. The remaining 20% of the film is developed by Carla, and
her customers are only satisfied 75% of the time. If you recently took your film to Photo
Max to be developed, what is the probability that Carla developed it if you are satisfied?
13)
14) A production process of computer parts uses two machines, one old machine and one new
machine. If the old machine is used, the probability that a defective part is produced is
0.13. If the new machine is used, the probability that a defective part is produced is 0.04.
Moreover, the new machine produces parts 4 times as fast as the old machine does. What
is the probability that a randomly selected part produced by this process is defective?
14)
15) A production process of computer parts uses two machines, one old machine and one new
machine. If the old machine is used, the probability that a defective part is produced is
0.13. If the new machine is used, the probability that a defective part is produced is 0.04.
Moreover, the new machine produces parts 4 times as fast as the old machine does. When
a defective part is produced, what is the probability that the old machine was used?
15)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
16) 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.
Given that a randomly selected component is defective, what is the probability it came from
shipment II? Assume that it is equally likely that the component came from shipment I as from
shipment II.
A) 0.384
B) 0.714
C) 0.2
D) 0.5
E) 0.286
16)
17) An online clothing store carries three brands of jeans. 40% of their jean sales are brand A, 20% are
brand B and the remainder are brand C. 20% of brand A’s jeans cost over $100, 40% of brand B’s
jeans cost over $100 and 90% of brand C’s jeans cost over $100. Given that a pair of jeans is
purchased for over $100, what is the probability that they are brand A?
A) 0.08
B) 0.154
C) 0.133
D) 0.4
E) 0.148
17)
7
18) The first two columns of the table below give a percentage distribution for adults in one city by
income group. The third column gives the percentage of people in each income group who plan to
buy a new car next year.
Income
(dollars)
0 - 4999
5000 - 9999
10,000 - 14,999
15,000 - 19,999
20,000 - 24,999
25,000 - 29,999
30,000 - 34,999
35,000 - 39,999
40,000 - 49,999
50,000 and over
Percentage
of population
5.2
6.4
5.4
8.7
9.4
10.2
13.8
10.7
15.5
14.7
18)
Percentage that will
buy new car next year
2
3
6
7
9
10
11
13
15
19
An adult is picked at random from the city. Given that the person selected plans to buy a new car
next year, what is the probability that their income is between $5000 and $9999?
A) 0.04
B) 0.03
C) 0.01
D) 0.05
E) 0.02
19) The first two columns of the table below give a percentage distribution for adults in one city by
income group. The third column gives the percentage of people in each income group who plan to
buy a new car next year.
Income
(dollars)
0 - 4999
5000 - 9999
10,000 - 14,999
15,000 - 19,999
20,000 - 24,999
25,000 - 29,999
30,000 - 34,999
35,000 - 39,999
40,000 - 49,999
50,000 and over
Percentage
of population
5.2
6.4
5.4
8.7
9.4
10.2
13.8
10.7
15.5
14.7
Percentage that will
buy new car next year
2
3
6
7
9
10
11
13
15
19
An adult is picked at random from the city. Given that the person selected plans to buy a new car
next year, what is the probability that their income is $50,000 or over?
A) 0.21
B) 0.25
C) 0.24
D) 0.22
E) 0.28
8
19)
Answer Key
Testname: 5_4
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
C
B
A
C
D
A
E
B
B
A
A
D
P(C|S) = 0.1599
P(D) = P(N and D) + P(O and D) = 0.032 + 0.026 = 0.058
P(O|D) = P(O and D)/P(D) = 0.026/0.058 = 0.448
B
B
E
B
9