Elementary Statistics Picturing The World 6th Edition By Larson -Test Bank
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Sample Test
Ch. 3 Probability
3.1 Basic Concepts of
Probability and Counting
1 Find Probabilities
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
1) A coin is tossed.
Find the probability that the result is heads.
A) 0.5 B) 0.1 C) 0.9
D) 1
2) A single six-sided
die is rolled. Find the probability of rolling a number less than 3.
A) 0.333 B) 0.1 C) 0.5
D) 0.25
3) A single six-sided
die is rolled. Find the probability of rolling a seven.
A) 0 B) 0.1 C) 0.5 D)
1
4) A study of 1000
randomly selected flights of a major airline showed that 769 of the flights
arrived on time.
What is the probability
of a flight arriving on time?
A) 769
1000
B) 231
1000
C) 1000
231
D) 1000
769
5) If one card is
drawn from a standard deck of 52 playing cards, what is the probability of
drawing an ace?
A) 1
13
B) 1
52
C) 14
D) 12
6) If one card is
drawn from a standard deck of 52 playing cards, what is the probability of
drawing a red card?
A) 12
B) 1
52
C) 14
D) 1
13
7) If one card is
drawn from a standard deck of 52 playing cards, what is the probability of
drawing a heart?
A) 14
B) 12
C) 34
D) 1
8) In a survey of
college students, 824 said that they have cheated on an exam and 1727 said that
they have not. If
one college student is
selected at random, find the probability that the student has cheated on an
exam.
A) 824
2551
B) 1727
2551
C) 2551
824
D) 2551
1727
9) If an individual is
selected at random, what is the probability that he or she has a birthday in
July? Ignore leap
years.
A) 31
365
B) 1
365
C) 364
365
D) 12
365
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SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
10) The data in the
table represent the number of consumer complaints against major U.S. airlines.
If one complaint
from the table is
randomly selected, find the probability that it was filed against United
Airlines.
Airline Number of
Complaints
United 1172
Northwest 765
Continental 563
11) The data in the
table represent the number of consumer complaints against major U.S. airlines.
If one complaint
from the table is
randomly selected, find the probability that it was filed against Northwest
Airlines.
Airline Number of
Complaints
United 1172
Northwest 765
Continental 563
12) The data in the
table represent the number of consumer complaints against major U.S. airlines.
If one complaint
from the table is
randomly selected, find the probability that it was filed against Continental
Airlines.
Airline Number of
Complaints
United 1172
Northwest 765
Continental 563
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
13) The distribution
of blood types for 100 Americans is listed in the table. If one donor is
selected at random, find
the probability of
selecting a person with blood type A+.
Blood Type O+ O- A+ A-
B+ B- AB+ ABNumber
37 6 34 6 10 2 4 1
A) 0.34 B) 0.4 C) 0.45
D) 0.68
14) The distribution
of blood types for 100 Americans is listed in the table. If one donor is
selected at random, find
the probability of
selecting a person with blood type A+ or A-.
Blood Type O+ O- A+ A-
B+ B- AB+ ABNumber
37 6 34 6 10 2 4 1
A) 0.4 B) 0.34 C) 0.02
D) 0.06
15) The distribution
of blood types for 100 Americans is listed in the table. If one donor is
selected at random, find
the probability of not
selecting a person with blood type B+.
Blood Type O+ O- A+ A-
B+ B- AB+ ABNumber
37 6 34 6 10 2 4 1
A) 0.90 B) 0.82 C)
0.12 D) 0.10
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16) The distribution
of blood types for 100 Americans is listed in the table. If one donor is
selected at random, find
the probability of selecting
a person with blood type AB-.
Blood Type O+ O- A+ A-
B+ B- AB+ ABNumber
37 6 34 6 10 2 4 1
A) 0.01 B) 0.05 C)
0.99 D) 0.10
17) The distribution
of Masterʹs degrees conferred by a university is listed in the table.
Major Frequency
Mathematics 216
English 207
Engineering 81
Business 176
Education 222
What is the
probability that a randomly selected student graduating with a Masterʹs degree
has a major of
Engineering? Round
your answer to three decimal places.
A) 0.090 B) 0.910 C)
0.012 D) 0.988
18) The distribution
of Masterʹs degrees conferred by a university is listed in the table.
Major Frequency
Mathematics 216
English 207
Engineering 86
Business 176
Education 227
What is the
probability that a randomly selected student graduating with a Masterʹs degree
has a major of
Education? Round your
answer to three decimal places.
A) 0.249 B) 0.751 C)
0.004 D) 0.331
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
19) Use the following
graph, which shows the types of incidents encountered with drivers using cell
phones, to
find the probability
that a randomly chosen incident involves cutting off a car. Round your answer
to three
decimal places.
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20) Use the following
graph, which shows the types of incidents encountered with drivers using cell
phones, to
find the probability
that a randomly chosen incident did not involve cutting off a car. Round your
answer to
three decimal places.
21) Use the pie chart,
which shows the number of Congressional Medal of Honor recipients in the United
States, to
find the probability
that a randomly chosen recipient served in the Navy.
22) Use the pie chart,
which shows the number of Congressional Medal of Honor recipients in the United
States, to
find the probability
that a randomly chosen recipient did not serve in the Marines.
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MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
23) A question has
five multiple-choice answers. Find the probability of guessing an incorrect
answer.
A) 45
B) 52
C) 15
D) 35
24) A question has
five multiple-choice questions. Find the probability of guessing the correct
answer.
A) 15
B) 54
C) 45
D) 25
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
25) The distribution
of Masterʹs degrees conferred by a university is listed in the table.
Major Frequency
Mathematics 216
English 207
Engineering 86
Business 176
Education 222
Find the probability
of randomly choosing a person graduating with a Masterʹs degree who did not
major in
Education. Round your
answer to three decimal places.
26) The data in the
table represent the number of consumer complaints against major U.S. airlines.
If one complaint
from the table is
randomly selected, find the probability that it was not filed against
Continental Airlines.
(Round to three
decimal places.)
Airline Number of
Complaints
United 287
Northwest 256
Continental 202
2 Identify the Sample
Space
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
Provide an appropriate
response.
27) Identify the
sample space of the probability experiment: shooting a free throw in basketball.
28) Identify the
sample space of the probability experiment: answering a true or false question
29) Identify the
sample space of the probability experiment: recording the number of days it
snowed in Cleveland
in the month of
January.
30) Identify the
sample space of the probability experiment: answering a multiple choice
question with A, B, C, and
D as the possible
answers
31) Identify the
sample space of the probability experiment: determining the childrenʹs gender
for a family of three
children (Use B for
boy and G for girl.)
32) Identify the
sample space of the probability experiment: rolling a single 12-sided die with
sides numbered 1-12
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33) Identify the
sample space of the probability experiment: rolling a pair of 12 -sided dice
(with sides numbered
1-12) and observing
the total number of points of each roll
34) Identify the
sample space of the probability experiment: A calculator has a function button
to generate a
random integer from -5
to 5
35) Identify the
sample space of the probability experiment: recording a response to the survey
question and the
gender of the
respondent.
36) Identify the
sample space of the probability experiment: recording the day of the week and
whether or not it
rains.
3 Identify Simple
Events
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Determine the number
of outcomes in the event. Then decide whether the event is a simple event or
not. Explain your
reasoning.
37) A computer is used
to randomly select a number between 1 and 1000. Event A is selecting a number
greater
than 600.
A) 400; Not a simple
event because it is an event that consists of more than a single outcome.
B) 1; Simple event
because it is an event that consists of a single outcome.
C) 600; Not a simple
event because it is an event that consists of more than a single outcome.
D) 400; Simple event
because only one number is selected.
38) You roll a
six-sided die. Event B is rolling an even number.
A) 3; Not a simple
event because it is an event that consists of more than a single outcome.
B) 1; Simple event
because it is an event that consists of a single outcome.
C) 2; Not a simple
event because it is an event that consists of more than a single outcome.
D) 3; Simple event
because the die is only rolled once.
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39) You randomly
select one card from a standard deck. Event B is selecting the ace of hearts.
A) 1; Simple event
because it is an event that consists of a single outcome.
B) 4; Simple event
because only one card is selected.
C) 4; Not a simple
event because it is an event that consists of more than a single outcome.
D) 13; Not a simple
event because it is an event that consists of more than a single outcome.
40) You randomly
select a computer from a batch of 50 which contains 3 defective computers.
Event B is selecting a
defective computer.
A) 3; Not a simple
event because it is an event that consists of more than a single outcome.
B) 3; Simple event because
it is an event that consists of only one type of computer.
C) 1; Simple event
because it is an event that consists of only one type of computer.
D) 50; Not a simple
event because it is an event that consists of more than a single outcome.
4 Use Fundamental
Counting Principle
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Use the fundamental
counting principle to solve the problem.
41) A shirt company
has 4 designs each of which can be made with short or long sleeves. There are 7
color patterns
available. How many
different shirts are available from this company?
A) 56 B) 28 C) 11 D)
13
42) If 5 newborn
babies are randomly selected, how many different gender sequences are possible?
A) 32 B) 10 C) 120 D)
25
43) A
singer-songwriter wishes to compose a melody. Each note in the melody must be
one of the 14 notes in her
vocal range. How many
different sequences of 3 notes are possible?
A) 2744 B) 4,782,969
C) 42 D) 2184
44) How many license
plates can be made consisting of 2 letters followed by 3 digits?
A) 676,000 B) 100,000
C) 11,881,376 D) 67,600
45) How many different
codes of 4 digits are possible if the first digit must be 3, 4, or 5 and if the
code may not end
in 0?
A) 2700 B) 300 C) 2999
D) 3000
5 Classify Types of
Probability
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
46) Classify the
statement as an example of classical probability, empirical probability, or
subjective probability.
The probability that a
train will be in an accident on a specific route is 1%.
A) empirical
probability B) classical probability C) subjective probability
47) Classify the
statement as an example of classical probability, empirical probability, or
subjective probability.
The probability that
interest rates will rise during the summer is 0.05.
A) subjective
probability B) classical probability C) empirical probability
48) Classify the
statement as an example of classical probability, empirical probability, or
subjective probability.
In Californiaʹs Pick
Three lottery, a person selects a 3-digit number. The probability of winning
Californiaʹs
Pick Three lottery is
1
1000
.
A) classical
probability B) empirical probability C) subjective probability
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49) Classify the
statement as an example of classical probability, empirical probability, or
subjective probability.
The probability that a
newborn baby is a boy is 12
.
A) classical
probability B) empirical probability C) subjective probability
50) Classify the
statement as an example of classical probability, empirical probability, or
subjective probability.
The probability that
it will rain tomorrow is 21%.
A) subjective
probability B) classical probability C) empirical probability
6 Determine Odds
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
51) The P(A) = 35
. Find the odds of
winning an A.
A) 3:2 B) 2:3 C) 3:5
D) 5:2
52) A card is picked
at random from a standard deck of 52 playing cards. Find the odds that it is
not a heart.
A) 3:1 B) 1:3 C) 4:1
D) 1:4
53) At the local
racetrack, the favorite in a race has odds 3:2 of winning. What is the probability
that the favorite
wins the race?
A) 0.6 B) 0.4 C) 0.2
D) 1.5
54) At the local
racetrack, the favorite in a race has odds 3:2 of losing. What is the
probability that the favorite wins
the race?
A) 0.4 B) 0.6 C) 0.2
D) 0.67
7 Concepts
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
55) Which of the
following cannot be a probability?
A) -68 B) 0 C) 0.001
D) 5
3
56) Which of the
following cannot be a probability?
A) 43
B) 0.0002 C) 1 D) 85%
57) Rank the
probabilities of 10%, 15, and 0.06 from the least likely to occur to the most
likely to occur.
A) 0.06, 10%, 15
B) 15
, 10%, 0.06 C) 0.06,
15
, 10% D) 10%, 15
, 0.06
58) Rank the
probabilities of 10%, 15
, and 0.06 from the
most likely to occur to the least likely to occur.
A) 15
, 10%, 0.06 B) 0.06,
10%, 15
C) 10%, 15
, 0.06 D) 0.06, 15
, 10%
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SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
59) Explain why the
following statement is incorrect:
He gave 110% effort.
3.2 Conditional
Probability and the Multiplication Rule
1 Determine Between
Independent and Dependent Events
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
1) Classify the events
as dependent or independent. Events A and B where
P(A) = 0.7, P(B) =
0.7, and P(A and B) = 0.49
A) independent B)
dependent
2) Classify the events
as dependent or independent. Events A and B where
P(A) = 0.8, P(B) =
0.1, and P(A and B) = 0.07
A) dependent B)
independent
3) Classify the events
as dependent or independent.
The events of getting
two aces when two cards are drawn from a deck of playing cards and the first
card is
replaced before the
second card is drawn.
A) independent B)
dependent
4) Classify the events
as dependent or independent. The events of getting two aces when two cards are
drawn
from a deck of playing
cards and the first card is not replaced before the second card is drawn.
A) dependent B)
independent
5) Classify the events
as dependent or independent. Event A: A red candy is selected from a package
with 30
colored candies and
eaten. Event B: A blue candy is selected from the same package and eaten.
A) dependent B)
independent
2 Find Conditional
Probabilities
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
6) A group of students
were asked if they carry a credit card. The responses are listed in the table.
Class
Credit Card
Carrier
Not a Credit Card
Carrier Total
Freshman 45 15 60
Sophomore 32 8 40
Total 77 23 100
If a student is
selected at random, find the probability that he or she owns a credit card
given that the student is
a freshman. Round your
answer to three decimal places.
A) 0.750 B) 0.250 C)
0.584 D) 0.450
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7) A group of students
were asked if they carry a credit card. The responses are listed in the table.
Class
Credit Card
Carrier
Not a Credit Card
Carrier Total
Freshman 17 43 60
Sophomore 28 12 40
Total 45 55 100
If a student is
selected at random, find the probability that he or she owns a credit card
given that the student is
a sophomore. Round
your answer to three decimal places.
A) 0.700 B) 0.300 C)
0.622 D) 0.280
8) A group of students
were asked if they carry a credit card. The responses are listed in the table.
Class
Credit Card
Carrier
Not a Credit Card
Carrier Total
Freshman 23 37 60
Sophomore 31 9 40
Total 54 46 100
If a student is
selected at random, find the probability that he or she is a freshman given
that the student owns
a credit card. Round
your answers to three decimal places.
A) 0.426 B) 0.383 C)
0.574 D) 0.230
9) A group of students
were asked if they carry a credit card. The responses are listed in the table.
Class
Credit Card
Carrier
Not a Credit Card
Carrier Total
Freshman 21 39 60
Sophomore 15 25 40
Total 36 64 100
If a student is
selected at random, find the probability that he or she is a sophomore given
that the student
owns a credit card.
Round your answers to three decimal places.
A) 0.417 B) 0.583 C)
0.900 D) 0.150
10) A group of
students were asked if they carry a credit card. The responses are listed in
the table.
Class
Credit Card
Carrier
Not a Credit Card
Carrier Total
Freshman 10 50 60
Sophomore 20 20 40
Total 30 70 100
If a student is
selected at random, find the probability that he or she is a sophomore and owns
a credit card.
Round your answers to
three decimal places.
A) 0.200 B) 0.333 C)
0.750 D) 0.667
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3 Use the
Multiplication Rule to Find Probabilities
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
11) You are dealt two
cards successively without replacement from a standard deck of 52 playing
cards. Find the
probability that the
first card is a two and the second card is a ten. Round your answer to three
decimal places.
A) 0.006 B) 0.994 C)
0.250 D) 0.500
12) Find the
probability of answering two true or false questions correctly if random
guesses are made. Only one of
the choices is
correct.
A) 0.25 B) 0.5 C) 0.75
D) 0.1
13) Find the
probability of answering the two multiple choice questions correctly if random
guesses are made.
Assume the questions
each have five choices for the answer. Only one of the choices is correct.
A) 0.04 B) 0.004 C)
0.4 D) 0.02
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
14) Find the
probability of getting four consecutive aces when four cards are drawn without
replacement from a
standard deck of 52
playing cards.
15) Find the
probability of selecting two consecutive threes when two cards are drawn
without replacement from a
standard deck of 52
playing cards. Round your answer to four decimal places.
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
16) A multiple-choice
test has five questions, each with five choices for the answer. Only one of the
choices is
correct. You randomly
guess the answer to each question. What is the probability that you answer the
first two
questions correctly?
A) 0.04 B) 0.2 C) 0.02
D) 0.4
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
17) A multiple-choice
test has five questions, each with five choices for the answer. Only one of the
choices is
correct. You randomly
guess the answer to each question. What is the probability that you answer all
five
questions correctly?
18) A multiple-choice
test has five questions, each with five choices for the answer. Only one of the
choices is
correct. You randomly
guess the answer to each question. What is the probability that you do not
answer any
of the questions
correctly?
19) A multiple-choice
test has five questions, each with five choices for the answer. Only one of the
choices is
correct. You randomly
guess the answer to each question. What is the probability that you answer at
least one
of the questions
correctly?
20) The probability it
will rain is 40% each day over a three-day period. What is the probability it
will rain at least
one of the three days?
21) The probability it
will rain is 40% each day over a three-day period. What is the probability it
will not rain at
least one of the three
days?
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MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
22) Four students
drive to school in the same car. The students claim they were late to school
and missed a test
because of a flat
tire. On the makeup test, the instructor asks the students to identify the tire
that went flat; front
driverʹs side, front
passengerʹs side, rear driverʹs side, or rear passengerʹs side. If the students
didnʹt really have
a flat tire and each
randomly selects a tire, what is the probability that all four students select
the same tire?
A) 1
64
B) 14
C) 1
256
D) 18
23) Find the
probability that of 25 randomly selected students, no two share the same
birthday.
A) 0.431 B) 0.995 C)
0.569 D) 0.068
24) Find the
probability that of 25 randomly selected students, at least two share the same
birthday.
A) 0.569 B) 0.068 C)
0.432 D) 0.995
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
25) What is the
probability that a husband, wife, and daughter have the same birthday?
4 Use Bayesʹs Theorem
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
26) Use Bayesʹ theorem
to solve this problem. A storeowner purchases stereos from two companies. From
Company A, 450 stereos
are purchased and 6% are found to be defective. From Company B, 550 stereos are
purchased and 4% are
found to be defective. Given that a stereo is defective, find the probability
that it came
from Company A.
A) 27
49
B) 33
49
C) 18
49
D) 22
49
27) Use Bayeʹs Theorem
to solve this problem, A paper bag contains two red balls and one blue ball. A
plastic bag
contains three blue
balls and one red ball. A coin is tossed. If it falls heads up, the paper bag
is selected and a
ball is drawn. If the
coin falls tails up, the plastic bag is selected and a ball is drawn. If a red
ball is selected,
what is the
probability that it came from the paper bag?
A) 8
11
B) 13
C) 18
D) 38
3.3 The Addition Rule
1 Determine if Events
Are Mutually Exclusive
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
1) Decide if the
events A and B are mutually exclusive or not mutually exclusive. A die is
rolled.
A: The result is an
odd number.
B: The result is an
even number.
A) mutually exclusive
B) not mutually exclusive
2) Decide if the
events A and B are mutually exclusive or not mutually exclusive, A die is
rolled.
A: The result is a 3.
B: The result is an
odd number.
A) not mutually
exclusive B) mutually exclusive
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3) Decide if the
events A and B are mutually exclusive or not mutually exclusive. A date in
Philadelphia is
selected.
A: It rains that day.
B: It snows that day.
A) not mutually
exclusive B) mutually exclusive
4) Decide if the
events A and B are mutually exclusive or not mutually exclusive. A card is
drawn from a standard
deck of 52 playing
cards.
A: The result is a 7.
B: The result is a
jack.
A) mutually exclusive
B) not mutually exclusive
5) Decide if the
events A and B are mutually exclusive or not mutually exclusive. A card is
drawn from a standard
deck of 52 playing
cards.
A: The result is a
club.
B: The result is a
king.
A) not mutually
exclusive B) mutually exclusive
6) Decide if the
events A and B are mutually exclusive or not mutually exclusive. A person is
selected at random.
A: Their birthday is
in the fall.
B: Their birthday is
in October.
A) not mutually
exclusive B) mutually exclusive
7) Decide if the
events A and B are mutually exclusive or not mutually exclusive. A student is
selected at random.
A: The student is
taking a math course.
B: The student is a
business major.
A) not mutually
exclusive B) mutually exclusive
2 Use the Addition
Rule to Find Probabilities
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
8) A card is drawn
from a standard deck of 52 playing cards. Find the probability that the card is
an ace or a king.
A) 2
13
B) 1
13
C) 4
13
D) 8
13
9) A card is drawn
from a standard deck of 52 playing cards. Find the probability that the card is
an ace or a heart.
A) 4
13
B) 7
52
C) 17
52
D) 3
13
10) A card is drawn
from a standard deck of 52 playing cards. Find the probability that the card is
an ace or a black
card.
A) 7
13
B) 15
26
C) 29
52
D) 4
13
11) The events A and B
are mutually exclusive. If P(A) = 0.6 and P(B) = 0.2, what is P(A or B)?
A) 0.8 B) 0 C) 0.12 D)
0.4
12) Given that P(A or
B) = 14
, P(A) = 17
, and P(A and B) = 19
, find P(B).
A) 55
252
B) 5
63
C) 127
252
D) 71
252
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SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
13) Use the following
graph, which shows the types of incidents encountered with drivers using cell
phones, to
find the probability
that a randomly chosen incident involves either swerving or almost hitting a
car.
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
14) The table lists
the smoking habits of a group of college students.
Sex Non-smoker Regular
Smoker Heavy Smoker Total
Man 135 51 5 191
Woman 187 21 12 220
Total 322 72 17 411
If a student is chosen
at random, find the probability of getting someone who is a regular or heavy
smoker.
Round your answer to
three decimal places.
A) 0.217 B) 0.708 C)
0.256 D) 0.153
15) The table lists
the smoking habits of a group of college students.
Sex Non-smoker Regular
Smoker Heavy Smoker Total
Man 135 70 5 210
Woman 187 21 15 223
Total 322 91 20 433
If a student is chosen
at random, find the probability of getting someone who is a man or a non
-smoker.
Round your answer to
three decimal places.
A) 0.917 B) 0.950 C)
0.942 D) 0.790
16) The table lists
the smoking habits of a group of college students.
Sex Non-smoker Regular
Smoker Heavy Smoker Total
Man 135 52 5 192
Woman 187 21 5 213
Total 322 73 10 405
If a student is chosen
at random, find the probability of getting someone who is a man or a woman.
Round
your answer to three
decimal places.
A) 1 B) 0.936 C) 0.795
D) 0.205
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17) The distribution
of Masterʹs degrees conferred by a university is listed in the table.
Assume that a student
majors in only one subject.
Major Frequency
Mathematics 229
English 203
Engineering 86
Business 176
Education 222
What is the
probability that a randomly selected student with a Masterʹs degree majored in
English or
Mathematics? Round
your answer to three decimal places.
A) 0.472 B) 0.528 C)
0.250 D) 0.222
18) One hundred people
were asked, ʺDo you favor the death penalty?ʺ Of the 33 that answered ʺyesʺ to
the
question, 14 were
male. Of the 67 that answered ʺnoʺ to the question, six were male. If one
person is selected at
random, what is the
probability that this person answered ʺyesʺ or was a male?
A) 0.39 B) 0.53 C)
0.67 D) 0.13
3 Use the Addition
Rule for Three Events
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
Provide an appropriate
response.
19) Use the pie chart,
which shows the number of Congressional Medal of Honor recipients, to find the
probability
that a randomly chosen
recipient served in the Army, Navy, or Marines.
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MULTIPLE CHOICE. Choose
the one alternative that best completes the statement or answers the question.
20) The distribution
of Masterʹs degrees conferred by a university is listed in the table.
Assume that a student
majors in only one subject.
Major Frequency
Mathematics 216
English 207
Engineering 77
Business 171
Education 220
What is the
probability that a randomly selected student with a Masterʹs degree majored in
Business, Education
or Engineering? Round
your answer to three decimal places.
A) 0.525 B) 0.475 C)
0.278 D) 0.333
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
21) In the Venn
diagram below, event A represents the adults who drink coffee, event B
represents the adults who
drink tea, and event C
represents the adults who drink cola. List the region(s) which represent the
adults who
drink both coffee and
tea.
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22) In the Venn
diagram below, event A represents the adults who drink coffee, event B
represents the adults who
drink tea, and event C
represents the adults who drink cola. List the region(s) which represent the
adults who
drink only cola.
4 Concepts
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
23) The events A and B
are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is P(A and B)?
A) 0 B) 0.12 C) 0.5 D)
0.7
3.4 Additional Topics
in Probability and Counting
1 Perform Calculations
with Permutations/Combinations
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Perform the indicated
calculation.
1) 5 P4
A) 120 B) 5 C) 24 D) 1
2) 8P4
A) 1680 B) 70 C) 2 D)
4
3) 10P2
A) 90 B) 45 C) 19 D) 8
4) 8C3
A) 56 B) 112 C) 3 D)
120
5) 6P4
9P3
A) 0.71 B) 0.18 C)
0.00050 D) 0.68
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6) 6C3
9C4
A) 0.16 B) 0.040 C)
0.0079 D) 8900
2 Distinguish
Permutations from Combinations
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
Decide if the
situation involves permutations, combinations, or neither. Explain your
reasoning.
7) The number of ways
6 friends can be seated in a row at a movie theater
8) The number of ways
a jury of 12 can be selected from a pool of 20
9) The number of
5-digit pin codes if no digit can be repeated
10) The number of ways
you can choose 4 books from a selection of 8 to bring on vacation
11) The number of ways
in which 5 contestants in a singing competition can finish
12) The number of ways
an airline can hire a flight attendant for its European flights, a flight
attendant for its
domestic flights, and
a flight attendant for its Asian flight from a pool of 35 applicants
13) The number of
five-letter passwords that can be created when letters can be repeated
3 Use Counting
Principles
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
Provide an appropriate
response.
14) The access code to
a houseʹs security system consists of eight digits. How many different codes
are available if
each digit can be
repeated?
A) 100,000,000 B)
16,777,216 C) 256 D) 8
15) A delivery route
must include stops at four cities. How many different routes are possible?
A) 24 B) 4 C) 16 D)
256
16) A tourist in
Ireland wants to visit six different cities. How many different routes are
possible?
A) 720 B) 120 C) 36 D)
46,656
17) Seven guests are
invited for dinner. How many ways can they be seated at a dinner table if the
table is straight
with seats only on one
side?
A) 5040 B) 40,320 C)
720 D) 1
18) The Environmental
Protection Agency must visit nine factories for complaints of air pollution. In
how many
different ways can a
representative visit five of these to investigate this week?
A) 15,120 B) 362,880
C) 5 D) 126
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
19) How many ways can
a jury of eight men and eight women be selected from twelve men and ten women?
20) How many ways can
two Republicans, one Democrat, and one Independent be chosen from nine
Republicans,
five Democrats, and
two Independents to fill four positions on city council?
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21) How many different
permutations of the letters in the word PROBABILITY are there?
22) How many different
permutations of the letters in the word STATISTICS are there?
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the question.
23) If a couple plans
to have nine children, how many gender sequences are possible?
A) 512 B) 9 C)
387,420,489 D) 81
24) If a couple has
six boys and six girls, how many gender sequences are possible?
A) 924 B) 12 C) 8 D)
16
SHORT ANSWER. Write the
word or phrase that best completes each statement or answers the question.
25) A student must
answer five questions on an exam that contains ten questions.
a) How many ways can
the student do this?
b) How many ways are
there if the student must answer the first and last question?
26) How many versions
of a test are required to cover all possible question arrangements if there are
nine
open-ended questions
on the test?
MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
27) How many ways can
five people, A, B, C, D, and E, sit in a row at a movie theater if A and B must
sit together?
A) 48 B) 120 C) 12 D)
24
28) How many ways can
five people, A, B, C, D, and E, sit in a row at a movie theater if C must sit
to the right of
but not necessarily
next to B?
A) 60 B) 24 C) 20 D)
48
29) How many ways can
five people, A, B, C, D, and E, sit in a row at a movie theater if D and E will
not sit next to
each other?
A) 72 B) 24 C) 48 D)
60
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
30) The access code to
a houseʹs security system consists of five digits. How many different codes are
available if
the first digit cannot
be zero and the arrangement of five fives is excluded?
31) In California,
each automobile license plate consists of a single digit followed by three
letters, followed by three
digits. How many
distinct license plates can be formed if there are no restrictions on the
digits or letters?
32) In California,
each automobile license plate consists of a single digit followed by three
letters, followed by three
digits. How many
distinct license plates can be formed if the first number cannot be zero and
the three letters
cannot form ʺGODʺ?
4 Use Counting Principles
to Find Probabilities
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
Provide an appropriate
response.
33) A certain code is
a sequence of 6 digits. What is the probability of generating 6 digits and
getting the code
consisting of 1,2,3, .
. ., 6 if each digit can be repeated?
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MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the
question.
34) A delivery route
must include stops at four cities. If the route is randomly selected, find the
probability that the
cities will be
arranged in alphabetical order. Round your answer to three decimal places.
A) 0.04166667 B)
0.00390625 C) 0.0625 D) 0.25
35) A tourist in
Ireland wants to visit four different cities. If the route is randomly
selected, what is the probability
that the tourist will
visit the cities in alphabetical order? Round your answer to three decimal
places.
A) 0.042 B) 0.167 C)
0.063 D) 0.250
SHORT ANSWER. Write
the word or phrase that best completes each statement or answers the question.
36) In the California
State lottery, you must select six numbers from fifty-two numbers to win the
big prize. The
numbers do not have to
be in a particular order. What is the probability that you will win the big
prize if you
buy one ticket?
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Ch. 3 Probability
Answer Key
3.1 Basic Concepts of
Probability and Counting
1 Find Probabilities
1) A
2) A
3) A
4) A
5) A
6) A
7) A
8) A
9) A
10) 1172
2500
11) 765
2500
12) 563
2500
13) A
14) A
15) A
16) A
17) A
18) A
19) 0.163
20) 0.837
21) 0.215
22) 0.914
23) A
24) A
25) Let E = Masterʹs
degree in Education.
P(E) = 222
907
. P(Eʹ ) = 1 – P(E) =
685
907
= 0.755
26) Let E = the event
the complaint was against Continental
P(E) = 202
745
P(Eʹ) = 1 – P(E) = 1 –
202
745
= 543
745
= 0.729
2 Identify the Sample
Space
27) {(hit, miss)}
28) {(true, false)}
29) {(0, 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, . . . , 30, 31)}
30) {(A, B, C, D)}
31) {(BBB), (BBG),
(BGB), (GBB), (BGG), (GBG), (GGB), (GGG)}
32) {(1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11, 12)}
33) {(2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24)}
34) {(-5, -4, -3, -2,
-1, 0, 1, 2, 3, 4, 5)}
35) {(YM, YF, NM, NF,
UM, UF)}
36) {(MR, TR, WR, HR,
FR, SAR, SUR, MN, TN, WN, HN, FN, SAN, SUN)}
3 Identify Simple
Events
37) A
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38) A
39) A
40) A
4 Use Fundamental
Counting Principle
41) A
42) A
43) A
44) A
45) A
5 Classify Types of Probability
46) A
47) A
48) A
49) A
50) A
6 Determine Odds
51) A
52) A
53) A
54) A
7 Concepts
55) A
56) A
57) A
58) A
59) Maximum effort is
100%.
3.2 Conditional
Probability and the Multiplication Rule
1 Determine Between
Independent and Dependent Events
1) A
2) A
3) A
4) A
5) A
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