Use the rule of total probability to find the indicated probability.
240)
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 50.0 75
African American 10.0 41
Hispanic 18.7 58
Asian 11.8 63
Other 9.5 50
An adult is selected at random from the city. Determine the probability that the adult obtained has
health insurance.
240)
A)
0.574
B)
0.646
C)
0.065
D)
0.599
Find the indicated probability by using the special addition rule.
241)
A relative frequency distribution is given below for the size of families in one U.S. city.
Size Relative frequency
20.432
30.223
40.198
50.101
60.028
7+0.018
A family is selected at random. Find the probability that the size of the family is between 2 and 5
inclusive. Round approximations to three decimal places.
241)
A)
0.533
B)
0.853
C)
0.954
D)
0.421
Use the general multiplication rule to find the indicated probability.
242)
A bag contains 9 red chips and 5 blue chips. Two chips are selected randomly without replacement
from the bag. What is the probability that the two chips are the same color?
242)
A)
0.505
B)
0.495
C)
0.582
D)
0.396
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.
243)
A bag contains 5 red chips and 7 blue chips. Two chips are selected randomly without replacement
from the bag. Draw a tree diagram for this problem.
243)
A)
Event Probability
4
11 (R & R) 0.152
5
12
7
11
(R & B) 0.265
(B & R) 0.265
7
12
5
11
6
11 (B & B) 0.318
B)
Event Probability
1
4(R & R) 0.050
1
5
1
7
(R & B) 0.029
(B & R) 0.029
1
7
1
5
1
6(B & B) 0.024
C)
Event Probability
5
12 (R & R) 0.174
5
12
7
12
(R & B) 0.243
(B & R) 0.243
7
12
5
12
7
12 (B & B) 0.340
Find the conditional probability.
244)
If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a “double”.
244)
A)
0.25
B)
0.5
C)
0.333
D)
0.167
List the outcomes comprising the specified event.
245)
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. The event A is defined as follows.
A = event that Helen gets first prize
List the outcomes that comprise the event (not A).
245)
A)
JG, JM, GJ, GM, MJ, MG
B)
JG, JH, JM, GJ, GH, GM, MJ
C)
HJ, HG, HM
D)
JG, JH, JM, GJ, GH, GM, MJ, MG, MH
Find the indicated probability by using the complementation rule.
246)
The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 400
21–24 408
25–28 268
29–32 140
33–36 107
37–40 53
Over 40 80
1456
A student from the community college is selected at random. Find the probability that the student
is 21 years or over. Give your answer as a decimal rounded to three decimal places.
246)
A)
0.670
B)
0.275
C)
0.280
D)
0.725
Find the indicated probability by using the general addition rule.
247)
In one city, 51.4% of adults are female, 8.1% of adults are left–handed, and 5.1% are left–handed
females. For an adult selected at random from the city, let
F = event the person is female
L = event the person is left–handed.
Find P(F or L). Round approximations to three decimal places.
247)
A)
0.492
B)
0.544
C)
0.676
D)
0.595
Find the indicated probability.
248)
If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH THT TTH TTT.
What is the probability of getting at least two tails?
248)
A)
1
2
B)
1
8
C)
3
8
D)
5
8
Use the general multiplication rule to find the indicated probability.
249)
An IRS auditor randomly selects 3 tax returns from 41 returns of which 11 contain errors. What is
the probability that she selects none of those containing errors?
249)
A)
0.0193
B)
0.3918
C)
0.0155
D)
0.3809
Use the basic counting rule to solve the problem.
250)
If 5 newborn babies are randomly selected, how many different gender sequences are possible?
250)
A)
120
B)
25
C)
32
D)
10
Determine whether the events are independent.
251)
A card is selected at random from a standard deck of 52 cards. Let
A = event the card is a club
B = event the card is a three.
Are A and B independent events?
251)
A)
Yes
B)
No
Find the indicated probability.
252)
The following contingency table provides a joint frequency distribution for a group of retired
people by career and age at retirement.
10 40 89 42 0.418
944 78 46 0.297
181 177 58 173 718
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.
252)
A)
0.418
B)
0.297
C)
0.124
D)
0.252
Solve the problem.
253)
How many 3–digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is
not allowed?
253)
A)
343
B)
5
C)
210
D)
6
Find the conditional probability.
254)
Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let
A = event a diamond is selected
B = event a club is selected.
Determine P (A | ( not B)).
254)
A)
0
B)
0.25
C)
1
D)
0.333
Provide an appropriate response.
255)
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 b is equal to 0.24, this can be interpreted as follows: 24% of the women who voted in
this election voted Republican?
255)
A)
True
B)
False
Find the conditional probability.
256)
In Anne’s community college, 42.2% of students are Asian and 3.6% are Asian chemistry majors.
What percentage of Asian students are chemistry majors?
256)
A)
45.8%
B)
11.7%
C)
38.6%
D)
8.5%
Use Bayes’s rule to find the indicated probability.
257)
A company is conducting a sweepstakes, and ships two boxes of game pieces to a particular store.
Box A has 4% of its contents being winners, while 2% of the contents of box B are winners. Box A
contains 29% of the total tickets. The contents of both boxes are mixed in a drawer and a ticket is
chosen at random. What is the probability it came from box A if it is a winner?
257)
A)
0.333
B)
0.009
C)
0.446
D)
0.667
Find the indicated probability by using the special addition rule.
258)
The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 401
21–25 407
26–30 206
31–35 57
Over 35 20
1091
A student from the community college is selected at random. Find the probability that the student
is between 26 and 35 inclusive. Round approximations to three decimal places.
258)
A)
0.241
B)
0.189
C)
0.052
D)
263
259)
A relative frequency distribution is given below for the size of families in one U.S. city.
Size Relative frequency
20.419
30.212
40.198
50.117
60.037
7+0.017
A family is selected at random. Find the probability that the size of the family is less than 5. Round
approximations to three decimal places.
259)
A)
0.527
B)
0.829
C)
0.410
D)
0.117
Use words or symbols, as indicated, to describe the event.
260)
The following contingency table provides a joint frequency distribution for a group of retired
people by age at retirement and career.
How many of these people were not attorneys when they retired?
260)
A)
165
B)
44
C)
690
D)
535
Provide an appropriate response.
261)
A person is selected at random from a certain population. Let
A = event the person is left–handed
B = event the person is male.
In terms of probability notation, the percentage of males in the population can be expressed as P(B).
Use probability notation to express the percentage of left–handed people in the population that are
male.
261)
A)
P(A|B)
B)
P(A&B)
C)
P(B|A)
D)
P(B)
Use Bayes’s rule to find the indicated probability.
262)
A person must select one of three boxes, each filled with clocks. The probability of box A being
selected is 0.28, of box B being selected is 0.16, and of box C being selected is 0.56. The probability
of finding a red clock in box A is 0.2, in box B is 0.4, and in box C is 0.9. A box is selected. Given that
the box contains a red clock, what is the probability that box A was chosen?
262)
A)
0.09
B)
0.28
C)
0.056
D)
0.133
Find the conditional probability.
263)
A frequency distribution is given below for the size of families in one U.S. city. Data are in
thousands, rounded to the nearest thousand.
Size No. of families
2800
3400
4295
5138
640
7+25
A family is selected at random. Find the conditional probability that the size of the family is less
than 6 given that it is at least 3.
263)
A)
0.529
B)
0.928
C)
0.491
D)
0.962
Find the indicated probability by using the special addition rule.
264)
A card is drawn from a well–shuffled deck of 52 cards. What is the probability of drawing a face
card or a 5?
264)
A)
16
B)
4
13
C)
2
13
D)
48
52
Determine the number of outcomes that comprise the specified event.
265)
The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 2069
21–25 2197
26–30 1106
31–35 838
Over 35 250
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 35 inclusive
B = event the student is 26 or over
Determine the number of outcomes that comprise the event (A & B).
265)
A)
6335
B)
2194
C)
1944
D)
4391
Solve the problem.
266)
How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to
choose from?
266)
A)
40,320
B)
20,160
C)
720
D)
48
267)
How many ways can an IRS auditor select 4 of 10 tax returns for an audit?
267)
A)
210
B)
24
C)
5040
D)
10,000
Provide an appropriate response.
268)
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 b is equal to 0.24, this can be interpreted as follows: 24% of the people who voted in
this election were women who voted Republican?
268)
A)
True
B)
False
Describe the specified event in words.
269)
When a quarter is tossed four times, 16 outcomes are possible.
HHHH HHHT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT
Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are
tails, and the fourth toss is heads. The events A and B are defined as follows.
A = event exactly two tails are tossed
B = event the last two tosses are heads
Describe the event (A & B) in words.
269)
A)
The event that two of the tosses come up tails and two tosses come up heads
B)
The event the first two tosses are tails and the last two tosses are heads
C)
The event that exactly two tails are tossed or the last two tosses are heads or both
D)
The event that the first two tosses come up the same and the last two tosses come up the same
Find the indicated probability by using the complementation rule.
270)
If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore
leap years.
270)
A)
0.917
B)
0.915
C)
0.093
D)
0.085
Find the conditional probability.
271)
If a single fair die is rolled, find the probability of a 5 given that the number rolled is odd.
271)
A)
0.667
B)
0.5
C)
0.167
D)
0.333
Draw a Venn diagram and shade the described events.
272)
From a finite sample, events A and B are mutually exclusive. Shade the collection A or B.
272)
A)
B)
C)
D)
Use the special multiplication rule to find the indicated probability.
273)
A family has five children. The probability of having a girl is 1/2. What is the probability of having
3 girls followed by 2 boys?
273)
A)
0.6252
B)
0.0625
C)
0.0313
D)
0.3125
Describe the specified event in words.
274)
When a quarter is tossed four times, 16 outcomes are possible.
HHHH HHHT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT
Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are
tails, and the fourth toss is heads. The event A is defined as follows.
A = event the first two tosses are heads
Describe the event (not A) in words.
274)
A)
The event that exactly one of the first two tosses is tails
B)
The event the last two tosses are heads
C)
The event the first two tosses are not both heads
D)
The event the first two tosses are tails
Estimate the probability of the event.
275)
A frequency distribution on employment information from Alpha Corporation follows.. Find the
probability that an employee has been with the company 10 years or less.
Years Employed No. of Employees
1–5 5
6–10 10
11–15 25
16–20 10
21–25 5
26–30 3
275)
A)
0.741
B)
0.294
C)
0.735
D)
0.259
Find the indicated probability by using the general addition rule.
276)
For a person selected randomly from a certain population, events A and B are defined as follows.
A = event the person is male
B = event the person is a smoker
For this particular population, it is found that P(A) =0.47,P(B) =0.29, and P(A & B) =0.15. Find
P(A or B). Round approximations to two decimal places.
276)
A)
0.47
B)
0.61
C)
0.76
D)
0.91
Estimate the probability of the event.
277)
A polling firm, hired to estimate the likelihood of the passage of an up–coming referendum,
obtained the set of survey responses to make its estimate. The encoding system for the data is:
0= FOR, 1= AGAINST. If the referendum were held today, find the probability that it would pass.
0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0
277)
A)
0.4
B)
0.65
C)
0.5
D)
0.6
Determine whether the events are mutually exclusive.
278)
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 events A, B, and C are defined as follows.
A = event the student took more than 9 hours
B = event the student took less than 6 hours
C = event the student took between 7 and
9 hours inclusive
Is the collection of events A, B, and C mutually exclusive?
278)
A)
Yes
B)
No
Use the basic counting rule to solve the problem.
279)
A singer–songwriter wishes to compose a melody. Each note in the melody must be one of the 12
notes in her vocal range. How many different sequences of 4 notes are possible?
279)
A)
20,736
B)
16,777,216
C)
11,880
D)
48
Find the indicated probability.
280)
A survey resulted in the sample data in the given table. If one of the survey respondents is
randomly selected, find the probability of getting someone who lives in a flat.
Type of
accommodation Number
House 476
Flat 689
Apartment 255
Other 621
280)
A)
0.485
B)
689
C)
0.001
D)
0.338
Find the indicated probability by using the complementation rule.
281)
A relative frequency distribution is given below for the size of families in one U.S. city.
Size Relative frequency
20.442
30.241
40.195
50.075
60.031
7+0.016
A family is selected at random. Find the probability that the size of the family is at least 3. Round
approximations to three decimal places.
281)
A)
0.241
B)
0.558
C)
0.683
D)
0.317
Use the general multiplication rule to find the indicated probability.
282)
You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing
cards. Find the probability that the first card is a king and the second card is a queen.
282)
A)
0.002
B)
0.127
C)
0.006
D)
0.154
Provide an appropriate response.
283)
A person is selected at random from a certain population. Let
A = event the person is left–handed
B = event the person is male.
In terms of probability notation, the percentage of males in the population can be expressed as P(B).
Use probability notation to express the percentage of males in the population that are left–handed.
283)
A)
P(A&B)
B)
P(B|A)
C)
P(A)
D)
P(A|B)