Download Probability

Exam
Name___________________________________
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) 1
C) 0.1
1)
D) 0.9
2) A single six-sided die is rolled. Find the probability of rolling a number less than 3.
A) 0.333
B) 0.5
C) 0.1
D) 0.25
2)
3) A single six-sided die is rolled. Find the probability of rolling a seven.
A) 1
B) 0.1
C) 0
3)
D) 0.5
4) A study of 1000 randomly selected flights of a major airline showed that 746 of the flights arrived
on time. What is the probability of a flight arriving on time?
500
500
373
127
B)
C)
D)
A)
373
127
500
500
4)
5) If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing
an ace?
1
1
1
1
B)
C)
D)
A)
13
4
52
2
5)
6) If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing a
red card?
1
1
1
1
B)
C)
D)
A)
2
52
4
13
6)
7) If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing a
heart?
1
3
1
B) 1
C)
D)
A)
2
4
4
7)
8) In a survey of college students, 890 said that they have cheated on an exam and 1719 said that they
have not. If one college student is selected at random, find the probability that the student has
cheated on an exam.
2609
1719
890
2609
B)
C)
D)
A)
1719
2609
2609
890
8)
9) If an individual is selected at random, what is the probability that he or she has a birthday in July?
Ignore leap years.
1
31
12
364
B)
C)
D)
A)
365
365
365
365
9)
1
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.
10)
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.
11)
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.
12)
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+.
13)
Blood Type O+ O- A+ A- B+ B- AB+ ABNumber
37
6
34
6
10
2
4
1
A) 0.4
B) 0.68
C) 0.45
D) 0.34
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) 0.02
B) 0.06
C) 0.4
2
D) 0.34
14)
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+.
15)
Blood Type O+ O- A+ A- B+ B- AB+ ABNumber
37
6
34
6
10
2
4
1
A) 0.82
B) 0.90
C) 0.10
D) 0.12
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-.
16)
Blood Type O+ O- A+ A- B+ B- AB+ ABNumber
37
6
34
6
10
2
4
1
A) 0.05
B) 0.01
C) 0.99
D) 0.10
17) The distribution of Masterʹs degrees conferred by a university is listed in the table.
17)
Major
Frequency
Mathematics
216
English
207
Engineering
85
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) 0.988
B) 0.094
C) 0.012
D) 0.906
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
254
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) 0.729
B) 0.004
C) 0.371
D) 0.271
3
18)
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.
19)
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.
20)
4
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.
21)
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.
22)
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.
5
4
1
3
B)
C)
D)
A)
2
5
5
5
23)
24) A question has five multiple-choice questions. Find the probability of guessing the correct answer.
2
1
5
4
A)
B)
C)
D)
5
5
4
5
24)
5
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.
25)
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.)
26)
Airline
Number of Complaints
United
287
Northwest
256
Continental
296
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
27) A coin is tossed. Find the probability that the result is heads.
A) 0.5
B) 1
C) 0.1
27)
D) 0.9
28) A single six-sided die is rolled. Find the probability of rolling a number less than 3.
A) 0.25
B) 0.333
C) 0.5
D) 0.1
28)
29) A single six-sided die is rolled. Find the probability of rolling a seven.
A) 0.5
B) 0
C) 1
29)
D) 0.1
30) 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?
1000
1000
769
231
B)
C)
D)
A)
769
231
1000
1000
30)
31) If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing
an ace?
1
1
1
1
B)
C)
D)
A)
52
2
4
13
31)
32) If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing a
red card?
1
1
1
1
B)
C)
D)
A)
13
2
4
52
32)
6
33) If one card is drawn from a standard deck of 52 playing cards, what is the probability of drawing a
heart?
3
1
1
B) 1
C)
D)
A)
4
2
4
33)
34) 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.
2551
2551
1727
824
B)
C)
D)
A)
1727
824
2551
2551
34)
35) If an individual is selected at random, what is the probability that he or she has a birthday in July?
Ignore leap years.
31
1
12
364
B)
C)
D)
A)
365
365
365
365
35)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
36) 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.
36)
Airline
Number of Complaints
United
1172
Northwest
765
Continental
563
37) 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.
37)
Airline
Number of Complaints
United
1172
Northwest
765
Continental
563
38) 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
7
38)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
39) 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+.
39)
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) 0.45
D) 0.68
40) 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-.
40)
Blood Type O+ O- A+ A- B+ B- AB+ ABNumber
37
6
34
6
10
2
4
1
A) 0.02
B) 0.34
C) 0.06
D) 0.4
41) 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+.
41)
Blood Type O+ O- A+ A- B+ B- AB+ ABNumber
37
6
34
6
10
2
4
1
A) 0.12
B) 0.82
C) 0.90
D) 0.10
42) 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-.
42)
Blood Type O+ O- A+ A- B+ B- AB+ ABNumber
37
6
34
6
10
2
4
1
A) 0.99
B) 0.05
C) 0.10
D) 0.01
43) 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) 0.012
B) 0.090
C) 0.910
D) 0.988
8
43)
44) The distribution of Masterʹs degrees conferred by a university is listed in the table.
44)
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) 0.331
B) 0.751
C) 0.004
D) 0.249
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
45) 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.
45)
46) 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.
46)
9
47) 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.
47)
48) 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.
48)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
49) A question has five multiple-choice answers. Find the probability of guessing an incorrect answer.
3
1
5
4
B)
C)
D)
A)
5
5
2
5
49)
50) A question has five multiple-choice questions. Find the probability of guessing the correct answer.
2
4
5
1
A)
B)
C)
D)
5
5
4
5
50)
10
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
51) The distribution of Masterʹs degrees conferred by a university is listed in the table.
51)
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.
52) 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.)
52)
Airline
Number of Complaints
United
287
Northwest
256
Continental
202
53) Identify the sample space of the probability experiment: shooting a free throw in
basketball.
53)
54) Identify the sample space of the probability experiment: answering a true or false question
54)
55) Identify the sample space of the probability experiment: recording the number of days it
snowed in Cleveland in the month of January.
55)
56) Identify the sample space of the probability experiment: answering a multiple choice
question with A, B, C, and D as the possible answers
56)
57) 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.)
57)
58) Identify the sample space of the probability experiment: rolling a single 12 -sided die with
sides numbered 1-12
58)
59) 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
59)
60) Identify the sample space of the probability experiment: A calculator has a function button
to generate a random integer from -5 to 5
60)
11
61) Identify the sample space of the probability experiment: recording a response to the
survey question and the gender of the respondent.
61)
62) Identify the sample space of the probability experiment: recording the day of the week
and whether or not it rains.
62)
63) Identify the sample space of the probability experiment: shooting a free throw in
basketball.
63)
64) Identify the sample space of the probability experiment: answering a true or false question
64)
65) Identify the sample space of the probability experiment: recording the number of days it
snowed in Cleveland in the month of January.
65)
66) Identify the sample space of the probability experiment: answering a multiple choice
question with A, B, C, and D as the possible answers
66)
67) 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.)
67)
68) Identify the sample space of the probability experiment: rolling a single 12 -sided die with
sides numbered 1-12
68)
69) 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
69)
70) Identify the sample space of the probability experiment: A calculator has a function button
to generate a random integer from -5 to 5
70)
12
71) Identify the sample space of the probability experiment: recording a response to the
survey question and the gender of the respondent.
71)
72) Identify the sample space of the probability experiment: recording the day of the week
and whether or not it rains.
72)
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.
73) A computer is used to randomly select a number between 1 and 1000. Event A is selecting a
73)
number greater than 600.
A) 400; Simple event because only one number is selected.
B) 400; Not a simple event because it is an event that consists of more than a single outcome.
C) 600; Not a simple event because it is an event that consists of more than a single outcome.
D) 1; Simple event because it is an event that consists of a single outcome.
74) You roll a six-sided die. Event B is rolling an even number.
A) 2; Not a simple event because it is an event that consists of more than a single outcome.
B) 3; Not a simple event because it is an event that consists of more than a single outcome.
C) 1; Simple event because it is an event that consists of a single outcome.
D) 3; Simple event because the die is only rolled once.
74)
75) You randomly select one card from a standard deck. Event B is selecting the ace of hearts.
A) 4; Not a simple event because it is an event that consists of more than a single outcome.
B) 13; Not a simple event because it is an event that consists of more than a single outcome.
C) 1; Simple event because it is an event that consists of a single outcome.
D) 4; Simple event because only one card is selected.
75)
13
76) 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) 1; Simple event because it is an event that consists of only one type of computer.
C) 50; Not a simple event because it is an event that consists of more than a single outcome.
D) 3; Simple event because it is an event that consists of only one type of computer.
76)
77) A computer is used to randomly select a number between 1 and 1000. Event A is selecting a
number greater than 600.
A) 400; Simple event because only one number is selected.
B) 600; Not a simple event because it is an event that consists of more than a single outcome.
C) 1; Simple event because it is an event that consists of a single outcome.
D) 400; Not a simple event because it is an event that consists of more than a single outcome.
77)
78) You roll a six-sided die. Event B is rolling an even number.
A) 1; Simple event because it is an event that consists of a single outcome.
B) 2; Not a simple event because it is an event that consists of more than a single outcome.
C) 3; 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.
78)
79) You randomly select one card from a standard deck. Event B is selecting the ace of hearts.
A) 4; Simple event because only one card is selected.
B) 13; Not a simple event because it is an event that consists of more than a single outcome.
C) 4; Not a simple event because it is an event that consists of more than a single outcome.
D) 1; Simple event because it is an event that consists of a single outcome.
79)
80) You randomly select a computer from a batch of 50 which contains 3 defective computers. Event B
is selecting a defective computer.
A) 1; Simple event because it is an event that consists of only one type of computer.
B) 3; Not a simple event because it is an event that consists of more than a single outcome.
C) 50; Not a simple event because it is an event that consists of more than a single outcome.
D) 3; Simple event because it is an event that consists of only one type of computer.
80)
Use the fundamental counting principle to solve the problem.
81) A shirt company has 4 designs each of which can be made with short or long sleeves. There are 5
color patterns available. How many different shirts are available from this company?
A) 40
B) 11
C) 9
D) 20
81)
82) If 8 newborn babies are randomly selected, how many different gender sequences are possible?
A) 64
B) 16
C) 256
D) 40,320
82)
83) A singer-songwriter wishes to compose a melody. Each note in the melody must be one of the 10
notes in her vocal range. How many different sequences of 3 notes are possible?
A) 59,049
B) 30
C) 1000
D) 720
83)
84) How many license plates can be made consisting of 3 letters followed by 2 digits?
A) 175,760
B) 100,000
C) 1,757,600
D) 11,881,376
84)
14
85) 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) 3000
D) 2999
85)
86) 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) 11
B) 56
C) 13
D) 28
86)
87) If 5 newborn babies are randomly selected, how many different gender sequences are possible?
A) 120
B) 25
C) 10
D) 32
87)
88) 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) 2184
C) 42
D) 4,782,969
88)
89) How many license plates can be made consisting of 2 letters followed by 3 digits?
A) 100,000
B) 676,000
C) 11,881,376
D) 67,600
89)
90) 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) 2999
B) 3000
C) 300
D) 2700
90)
Provide an appropriate response.
91) Which of the following cannot be a probability?
A) 0
91)
5
C)
3
B) -68
D) 0.001
92)
92) Which of the following cannot be a probability?
A) 85%
4
C)
3
B) 0.0002
D) 1
1
93) Rank the probabilities of 10%, , and 0.06 from the least likely to occur to the most likely to occur.
5
1
A) 0.06, , 10%
5
B)
1
, 10%, 0.06
5
1
C) 10%, , 0.06
5
D) 0.06, 10%, 1
5
1
94) Rank the probabilities of 10%, , and 0.06 from the most likely to occur to the least likely to occur.
5
A)
1
, 10%, 0.06
5
1
B) 0.06, , 10%
5
1
C) 10%, , 0.06
5
D) 0.06, 10%, 1
5
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
95) Explain why the following statement is incorrect:
He gave 110% effort.
95)
15
93)
94)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
96) Classify the events as dependent or independent. Events A and B where P(A) = 0.4, P(B) = 0.9, and P(A and B) = 0.36
A) independent
B) dependent
96)
97) 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) = 0.48
A) independent
B) dependent
97)
98) 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) dependent
B) independent
98)
99) 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) independent
B) dependent
99)
100) 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) independent
B) dependent
100)
101) 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) dependent
B) independent
101)
102) 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
102)
103) 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
103)
104) 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
104)
105) 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) independent
B) dependent
105)
16
106) A group of students were asked if they carry a credit card. The responses are listed in the table.
Class
Freshman
Sophomore
Total
106)
Credit Card Not a Credit Card Carrier
Carrier
Total
45
15
60
5
35
40
50
50
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) 0.450
B) 0.250
C) 0.900
D) 0.750
107) A group of students were asked if they carry a credit card. The responses are listed in the table.
Class
Freshman
Sophomore
Total
107)
Credit Card Not a Credit Card Carrier
Carrier
Total
18
42
60
11
29
40
29
71
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) 0.110
B) 0.379
C) 0.275
D) 0.725
108) A group of students were asked if they carry a credit card. The responses are listed in the table.
Class
Freshman
Sophomore
Total
108)
Credit Card Not a Credit Card Carrier
Carrier
Total
14
46
60
32
8
40
46
54
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) 0.304
B) 0.233
C) 0.140
D) 0.696
109) A group of students were asked if they carry a credit card. The responses are listed in the table.
Class
Freshman
Sophomore
Total
Credit Card Not a Credit Card Carrier
Carrier
Total
23
37
60
8
32
40
31
69
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) 0.080
B) 0.742
C) 0.775
D) 0.258
17
109)
110) A group of students were asked if they carry a credit card. The responses are listed in the table.
Class
Freshman
Sophomore
Total
110)
Credit Card Not a Credit Card Carrier
Carrier
Total
11
49
60
16
24
40
27
73
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) 0.593
B) 0.675
C) 0.407
D) 0.160
111) A group of students were asked if they carry a credit card. The responses are listed in the table.
Class
Freshman
Sophomore
Total
111)
Credit Card Not a Credit Card Carrier
Carrier
Total
45
15
60
32
8
40
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) 0.250
B) 0.450
C) 0.750
D) 0.584
112) A group of students were asked if they carry a credit card. The responses are listed in the table.
Class
Freshman
Sophomore
Total
112)
Credit Card Not a Credit Card Carrier
Carrier
Total
17
43
60
28
12
40
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) 0.622
B) 0.280
C) 0.700
D) 0.300
113) A group of students were asked if they carry a credit card. The responses are listed in the table.
Class
Freshman
Sophomore
Total
Credit Card Not a Credit Card Carrier
Carrier
Total
23
37
60
31
9
40
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) 0.383
B) 0.426
C) 0.230
D) 0.574
18
113)
114) A group of students were asked if they carry a credit card. The responses are listed in the table.
Class
Freshman
Sophomore
Total
114)
Credit Card Not a Credit Card Carrier
Carrier
Total
21
39
60
15
25
40
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) 0.583
B) 0.417
C) 0.150
D) 0.900
115) A group of students were asked if they carry a credit card. The responses are listed in the table.
Class
Freshman
Sophomore
Total
115)
Credit Card Not a Credit Card Carrier
Carrier
Total
10
50
60
20
20
40
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) 0.667
B) 0.200
C) 0.750
D) 0.333
116) 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) 0.500
B) 0.994
C) 0.250
D) 0.006
116)
117) Find the probability of answering two true or false questions correctly if random guesses are made.
Only one of the choices is correct.
A) 0.75
B) 0.25
C) 0.5
D) 0.1
117)
118) 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) 0.02
C) 0.004
D) 0.4
118)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
119) Find the probability of getting four consecutive aces when four cards are drawn without
replacement from a standard deck of 52 playing cards.
119)
120) 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.
120)
19
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
121) 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) 0.2
B) 0.02
C) 0.04
D) 0.4
121)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
122) 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?
122)
123) 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?
123)
124) 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?
124)
125) 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?
125)
126) 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?
126)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
127) 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?
1
1
1
1
B)
C)
D)
A)
8
256
4
64
127)
128) Find the probability that of 25 randomly selected students, no two share the same birthday.
A) 0.569
B) 0.995
C) 0.068
D) 0.431
128)
129) Find the probability that of 25 randomly selected students, at least two share the same birthday.
A) 0.068
B) 0.569
C) 0.995
D) 0.432
129)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
130) What is the probability that a husband, wife, and daughter have the same birthday?
20
130)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
131) 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) 0.250
B) 0.500
C) 0.006
D) 0.994
131)
132) Find the probability of answering two true or false questions correctly if random guesses are made.
Only one of the choices is correct.
A) 0.75
B) 0.1
C) 0.25
D) 0.5
132)
133) 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) 0.4
C) 0.004
D) 0.02
133)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
134) Find the probability of getting four consecutive aces when four cards are drawn without
replacement from a standard deck of 52 playing cards.
134)
135) 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.
135)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
136) 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) 0.4
C) 0.2
D) 0.02
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
137) 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?
137)
138) 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?
138)
139) 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?
139)
140) 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?
140)
141) 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?
141)
21
136)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
142) 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?
1
1
1
1
B)
C)
D)
A)
256
8
4
64
142)
143) Find the probability that of 25 randomly selected students, no two share the same birthday.
A) 0.068
B) 0.569
C) 0.431
D) 0.995
143)
144) Find the probability that of 25 randomly selected students, at least two share the same birthday.
A) 0.068
B) 0.569
C) 0.995
D) 0.432
144)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
145) What is the probability that a husband, wife, and daughter have the same birthday?
145)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
146) 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) not mutually exclusive
B) mutually exclusive
146)
147) 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
147)
148) 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
148)
149) 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) not mutually exclusive
B) mutually exclusive
149)
150) 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
150)
22
151) 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
151)
152) 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
152)
153) 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
153)
154) 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
154)
155) 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
155)
156) 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) not mutually exclusive
B) mutually exclusive
156)
157) 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) mutually exclusive
B) not mutually exclusive
157)
158) 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
158)
23
159) 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
159)
160) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an
ace or a king.
1
8
4
2
B)
C)
D)
A)
13
13
13
13
160)
161) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an
ace or a heart.
3
7
17
4
B)
C)
D)
A)
13
52
52
13
161)
162) 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.
7
29
4
15
B)
C)
D)
A)
13
52
13
26
162)
163) The events A and B are mutually exclusive. If P(A) = 0.1 and P(B) = 0.2, what is P(A or B)?
A) 0.02
B) 0.1
C) 0
D) 0.3
163)
1
1
1
164) Given that P(A or B) = , P(A) = , and P(A and B) = , find P(B).
2
6
8
A)
11
24
B)
13
24
C)
19
24
164)
D)
1
6
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
165) 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.
24
165)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
166) The table lists the smoking habits of a group of college students.
166)
Sex
Non-smoker Regular Smoker Heavy Smoker Total
Man
135
59
5
199
Woman
187
21
8
216
Total
322
80
13
415
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) 0.161
B) 0.224
C) 0.267
D) 0.720
167) The table lists the smoking habits of a group of college students.
167)
Sex
Non-smoker Regular Smoker Heavy Smoker Total
Man
135
34
5
174
Woman
187
21
10
218
Total
322
55
15
392
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) 0.945
B) 0.941
C) 0.921
D) 0.860
168) The table lists the smoking habits of a group of college students.
168)
Sex
Non-smoker Regular Smoker Heavy Smoker Total
Man
135
31
5
171
Woman
187
21
13
221
Total
322
52
18
392
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) 0.821
C) 0.913
D) 0.179
169) 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
224
English
202
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) 0.246
B) 0.222
C) 0.468
D) 0.532
25
169)
170) 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) 0.13
B) 0.39
C) 0.67
D) 0.53
170)
171) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an
ace or a king.
1
4
2
8
B)
C)
D)
A)
13
13
13
13
171)
172) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an
ace or a heart.
4
17
7
3
B)
C)
D)
A)
13
52
52
13
172)
173) 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.
15
29
7
4
B)
C)
D)
A)
26
52
13
13
173)
174) 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) 0.12
B) 0.4
C) 0.8
D) 0
174)
1
1
1
175) Given that P(A or B) = , P(A) = , and P(A and B) = , find P(B).
4
7
9
A)
71
252
B)
127
252
C)
55
252
175)
D)
5
63
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
176) 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.
26
176)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
177) The table lists the smoking habits of a group of college students.
177)
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) 0.708
B) 0.256
C) 0.217
D) 0.153
178) The table lists the smoking habits of a group of college students.
178)
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) 0.950
B) 0.917
C) 0.790
D) 0.942
179) The table lists the smoking habits of a group of college students.
179)
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) 0.936
B) 0.205
C) 1
D) 0.795
180) 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) 0.222
B) 0.528
C) 0.472
D) 0.250
27
180)
181) 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) 0.13
C) 0.67
D) 0.53
181)
182) 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) 0.7
B) 0.12
C) 0
D) 0.5
182)
Perform the indicated calculation.
183) 6 P4
A) 24
183)
B) 30
C) 2
D) 360
184) 10P5
A) 2
B) 30,240
C) 252
D) 5
185) 10P4
A) 34
B) 6
C) 210
D) 5040
186) 10C4
A) 210
B) 1260
C) 720
D) 3
187)
185)
186)
6 P4
187)
11P3
A) 0.0000045
188)
184)
B) 0.091
C) 0.35
D) 0.36
5 C2
188)
10C3
A) 0.028
B) 140,000
C) 0.083
D) 0.000099
189) 5 P4
A) 24
B) 120
C) 5
D) 1
190) 8 P4
A) 4
B) 2
C) 70
D) 1680
191) 10P2
A) 90
B) 8
C) 45
D) 19
192) 8 C3
A) 3
B) 120
C) 112
D) 56
189)
190)
191)
192)
28
193)
6 P4
A) 0.18
194)
193)
9 P3
B) 0.00050
C) 0.68
D) 0.71
6 C3
194)
9 C4
A) 0.040
B) 0.16
C) 0.0079
29
D) 8900
Answer Key
Testname: MATH212CH3_PROBABILITY
1)
2)
3)
4)
5)
6)
7)
8)
9)
A
A
C
D
B
B
A
D
C
1172
10)
2500
11)
765
2500
12)
563
2500
13) D
14) C
15) B
16) B
17) B
18) D
19) 0.163
20) 0.837
21) 0.215
22) 0.914
23) C
24) B
25) Let E = Masterʹs degree in Education.
685
222
. P(Eʹ ) = 1 - P(E) = = 0.755
P(E) = 907
907
26) Let E = the event the complaint was against Continental
296
P(E) = 839
P(Eʹ) = 1 - P(E) = 1 - 296 543
= = 0.647
839 839
27) A
28) B
29) B
30) D
31) A
32) C
33) A
34) A
35) B
1172
36)
2500
37)
765
2500
30
Answer Key
Testname: MATH212CH3_PROBABILITY
38)
563
2500
39) B
40) D
41) C
42) D
43) B
44) D
45) 0.163
46) 0.837
47) 0.215
48) 0.914
49) A
50) D
51) Let E = Masterʹs degree in Education.
685
222
. P(Eʹ ) = 1 - P(E) = = 0.755
P(E) = 907
907
52) Let E = the event the complaint was against Continental
202
P(E) = 745
P(Eʹ) = 1 - P(E) = 1 - 202 543
= = 0.729
745 745
53) {(hit, miss)}
54) {(true, false)}
55) {(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, . . . , 30, 31)}
56) {(A, B, C, D)}
57) {(BBB), (BBG), (BGB), (GBB), (BGG), (GBG), (GGB), (GGG)}
58) {(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)}
59) {(2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24)}
60) {(-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)}
61) {(YM, YF, NM, NF, UM, UF)}
62) {(MR, TR, WR, HR, FR, SAR, SUR, MN, TN, WN, HN, FN, SAN, SUN)}
63) {(hit, miss)}
64) {(true, false)}
65) {(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, . . . , 30, 31)}
66) {(A, B, C, D)}
67) {(BBB), (BBG), (BGB), (GBB), (BGG), (GBG), (GGB), (GGG)}
68) {(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)}
69) {(2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24)}
70) {(-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)}
71) {(YM, YF, NM, NF, UM, UF)}
72) {(MR, TR, WR, HR, FR, SAR, SUR, MN, TN, WN, HN, FN, SAN, SUN)}
73) B
74) B
75) C
76) A
77) D
78) C
79) D
31
Answer Key
Testname: MATH212CH3_PROBABILITY
80) B
81) A
82) C
83) C
84) C
85) A
86) B
87) D
88) A
89) B
90) D
91) B
92) C
93) D
94) A
95) Maximum effort is 100%.
96) A
97) B
98) B
99) B
100) B
101) B
102) A
103) A
104) A
105) B
106) D
107) C
108) A
109) D
110) D
111) C
112) C
113) B
114) B
115) B
116) D
117) B
118) A
4 3 2 1
= 0.00000369
119) P(4-Aces) = 52 51 50 49
120) P(2-threes) = 4 3
= 0.0045
52 51
121) C
122) P(all five questions answered correctly) = 123) P(all five questions answers incorrect) = 1 1 1 1 1
= 0.00032
5 5 5 5 5
4 4 4 4 4
= 0.32768
5 5 5 5 5
32
Answer Key
Testname: MATH212CH3_PROBABILITY
124) P(at least one correct)
= 1 - P(all five answers incorrect)
4 4 4 4 4
= 1 - 0.32768 = 0.67232
= 1 - 5 5 5 5 5
125) P(rain at least one day) = 1 - P(no rain all three days)
= 1 - (0.60)(0.60)(0.60)
= 0.784
126) P(not rain at least one day) = 1 - P(rain all three days)
= 1 - (0.40)(0.40)(0.40)
= 0.936
127) A
128) D
129) B
365 1
1
= 0.00000751
130)
365 365 365
131) C
132) C
133) A
134) P(4-Aces) = 4 3 2 1
= 0.00000369
52 51 50 49
135) P(2-threes) = 4 3
= 0.0045
52 51
136) A
137) P(all five questions answered correctly) = 138) P(all five questions answers incorrect) = 139) P(at least one correct)
1 1 1 1 1
= 0.00032
5 5 5 5 5
4 4 4 4 4
= 0.32768
5 5 5 5 5
= 1 - P(all five answers incorrect)
4 4 4 4 4
= 1 - 0.32768 = 0.67232
= 1 - 5 5 5 5 5
140) P(rain at least one day) = 1 - P(no rain all three days)
= 1 - (0.60)(0.60)(0.60)
= 0.784
141) P(not rain at least one day) = 1 - P(rain all three days)
= 1 - (0.40)(0.40)(0.40)
= 0.936
142) A
143) C
144) B
365 1
1
145)
= 0.00000751
365 365 365
146)
147)
148)
149)
150)
151)
152)
153)
B
A
A
B
A
A
A
A
33
Answer Key
Testname: MATH212CH3_PROBABILITY
154)
155)
156)
157)
158)
159)
160)
161)
162)
163)
164)
165)
166)
167)
168)
169)
170)
171)
172)
173)
174)
175)
176)
177)
178)
179)
180)
181)
182)
183)
184)
185)
186)
187)
188)
189)
190)
191)
192)
193)
194)
A
A
B
B
A
A
A
A
B
D
A
0.512
B
C
A
C
B
D
B
D
C
C
0.512
C
B
C
C
A
C
D
B
D
A
D
C
B
D
A
D
D
B
34