Use words or symbols, as indicated, to describe the event.
57)
The following contingency table provides a joint frequency distribution for the popular votes cast
in the presidential election by region and political party. Data are in thousands, rounded to the
nearest thousand.
Suppose a person who voted in the presidential election is selected at random. Describe in words
the event P2.
57)
A)
The person selected was in the Midwest.
B)
The person selected voted Republican.
C)
The person selected voted Republican and was in the Midwest.
D)
The person selected voted Democrat.
Use Bayes’s rule to find the indicated probability.
58)
In one town, 8% of 18–29 year olds own a house, as do 34% of 30–50 year olds and 52% of those
over 50. According to a recent census taken in the town, 28.5% of adults in the town are 18–29 years
old, 36.8% are 30–50 years old, and 34.7% are over 50. What percentage of house–owners are 30–50
years old?
58)
A)
36.9
B)
12.5
C)
34
D)
36.8
Find the indicated probability by using the complementation rule.
59)
The distribution of B.A. degrees conferred by a local college is listed below, by major.
Major Frequency
English 2073
Mathematics 2164
Chemistry 318
Physics 856
Liberal Arts 1358
Business 1676
Engineering 868
9313
What is the probability that a randomly selected degree is not in Mathematics?
59)
A)
0.682
B)
0.303
C)
0.768
D)
0.232
Use counting rules to determine the probability.
60)
8 basketball players are to be selected to play in a special game. The players will be selected from a
list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest
players will be selected?
60)
A)
1
2,220,075
B)
8
27
C)
1
40,320
D)
1
213,127,200
Use the basic counting rule to solve the problem.
61)
Mark can remember only the first 4 digits of his friend’s phone number. He also knows that the
number has 7 digits and that the last digit is not a 0. If Mark were to dial all of the possible numbers
and if it takes him 22 seconds to try each one, how long would it take to try every possibility?
61)
A)
366.7 minutes
B)
330 minutes
C)
36.7 minutes
D)
11 minutes
Find the indicated probability.
62)
The distribution of B.A. degrees conferred by a local college is listed below, by major.
Major Frequency
English 2073
Mathematics 2164
Chemistry 318
Physics 856
Liberal Arts 1358
Business 1676
Engineering 868
9313
What is the probability that a randomly selected degree is in Engineering?
62)
A)
0.1028
B)
868
C)
0.0932
D)
0.0012
Describe the specified event in words.
63)
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 first toss is heads
Describe the event (A or B) in words.
63)
A)
Event that exactly two tails are tossed and the first toss is heads
B)
Event that the first toss is heads or the last two tosses are tails or both
C)
Event that exactly two tails are tossed or the first toss is heads or both
D)
Event that exactly two tails are tossed or the first toss is heads but not both
64)
The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 4946
21–25 4808
26–30 2673
31–35 2036
Over 35 525
A student from the community college is selected at random. The event A is defined as follows.
A = event the student is between 26 and 35 inclusive.
Describe the event (not A) in words.
64)
A)
The event the student is under 26 and over 35
B)
The event the student is under 26 or over 35
C)
The event the student is over 35
D)
The event the student is at most 26 or at least 35
Use the general multiplication rule to find the indicated probability.
65)
What is the probability that 4 randomly selected people all have different birthdays?
65)
A)
0.9918
B)
0.9891
C)
0.9729
D)
0.9836
Evaluate the expression.
66)
8C0
66)
A)
5040
B)
7
C)
8
D)
1
67)
22C1
67)
A)
23
B)
1
C)
21
D)
22
Determine whether the events are mutually exclusive.
68)
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 heads are tossed
B = event all four tosses come up the same
Are the events A and B mutually exclusive?
68)
A)
Yes
B)
No
Provide an appropriate response.
69)
Students at a local university were asked if they knew about Bayes’s Rule. Assume the following:
B1= event the student did not know about Bayes’s Rule.
B2= event the student did know about Bayes’s Rule.
S = event the student was in a statistics class.
Of those who knew about Bayes’s Rule, let S1= event the student was in a statistics class. Of those
who did not know about Bayes’s Rule, let S2= event the student was in a statistics class. Using
probability notation, describe the prior probability that a student did not know about Bayes’s Rule.
69)
A)
P(B1)
B)
P(B1|S2)
C)
P(B2)
D)
P(B1|S1)
Determine whether the events are mutually exclusive.
70)
A card is selected randomly from a deck of 52. The events A, B, and C are defined as follows.
A = event the card selected is a heart
B = event the card selected is a club
C = event the card selected is an ace
Is the collection of events A, B, and C mutually exclusive?
70)
A)
Yes
B)
No
List the outcomes comprising the specified event.
71)
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. List the outcomes that comprise the following event.
A = event that Helen gets a prize
71)
A)
JH, GH, HJ, HG, HM, MH
B)
JH, GH, HJ, JG, HG, HM, MH
C)
HJ, HG, HM
D)
JH, GH, HJ, HG, HM
Evaluate the expression.
72)
10P3
72)
A)
27
B)
720
C)
120
D)
7
Answer the question.
73)
In a certain town, 5% of people commute to work by bicycle. If a person is selected randomly from
the town, what are the odds against selecting someone who commutes by bicycle?
73)
A)
19 to 1
B)
1 to 20
C)
1 to 19
D)
19 to 20
Use the rule of total probability to find the indicated probability.
74)
Among students at one college are 3869 women and 3191 men. The following table provides
relative–frequency distributions for subject major for males and females at the college.
Major Relative frequency Relative frequency
for women for men
Humanities 0.183 0.155
Science 0.276 0.37
Social Science 0.127 0.14
Other 0.414 0.335
A student is selected at random from the college. Determine the probability that the student is a
science major.
74)
A)
0.328
B)
0.323
C)
0.151
D)
0.318
Use Bayes’s rule to find the indicated probability.
75)
The first two columns of the table below give a percentage distribution for adults in one city by
income group. The third column gives the percentage of people in each income group who plan to
buy a new car next year.
Income Percentage Percentage that will
(dollars) of population buy new car next year
0 – 4999 5.2 2
5000 – 9999 6.4 3
10,000 – 14,999 5.4 6
15,000 – 19,999 8.7 7
20,000 – 24,999 9.4 9
25,000 – 29,999 10.2 10
30,000 – 34,999 13.8 11
35,000 – 39,999 10.7 13
40,000 – 49,999 15.5 15
50,000 and over 14.7 19
An adult is picked at random from the city. Given that the person selected plans to buy a new car
next year, what is the probability that the person’s income is $50,000 or over?
75)
A)
0.28
B)
0.25
C)
0.22
D)
0.24
Use the basic counting rule to solve the problem.
76)
How many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if the
sequence may not end in 000? Repetition of digits is allowed.
76)
A)
2,000
B)
1,512
C)
2,997
D)
2,999
Find the indicated probability by using the general addition rule.
77)
Let A and B be events such that P(A) =1
5, P(A or B) =1
2, and P(A and B) =1
10 . Determine P(B).
77)
A)
4
5
B)
3
10
C)
1
10
D)
2
5
Evaluate the expression.
78)
10P5
78)
A)
5
B)
252
C)
2
D)
30,240
Find the conditional probability.
79)
Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let
A = event a queen is selected
B = event a diamond is selected.
Determine P(B|A).
79)
A)
0.25
B)
0.019
C)
0.077
D)
0.308
Solve the problem.
80)
A tourist in France wants to visit 10 different cities. How many different routes are possible?
80)
A)
362,880
B)
10
C)
100
D)
3,628,800
Use words or symbols, as indicated, to describe the event.
81)
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 store clerks when they retired?
81)
A)
54
B)
18
C)
182
D)
50
List the outcome(s) of the stated event.
82)
The odds against winning in a horse race are shown in the following table.
Horse #1 #2 #3 #4 #5 #6 #7
Odds 213 220 11 20 7
Based on these odds, which horses comprise: A = event one of the two long shots (least likely to
win) wins the race?
82)
A)
Horses #4 and #6
B)
Horses #1 and #2
C)
Horses #1 and #3
D)
Horse #1
Use the general multiplication rule to find the indicated probability.
83)
Among the contestants in a competition are 48 women and 21 men. If 5 winners are randomly
selected, what is the probability that they are all men?
83)
A)
0.01603
B)
0.00181
C)
0.01188
D)
0.16291
Use words or symbols, as indicated, to describe the event.
84)
The Book Industry Study Group, Inc., performs sample surveys to obtain information on
characteristics of book readers. A book reader is defined to be one who read one or more books in
the six months prior to the survey; a non–book reader is defined to be one who read newspapers or
magazines but no books in the six months prior to the survey; a nonreader is defined to be one who
did not read a book, newspaper, or magazine in the six months prior to the survey. The following
data were obtained from a random sample of 1429 persons 16 years old and over.
How may people made less than $40,000?
84)
A)
1125
B)
304
C)
313
D)
1429
Find the conditional probability.
85)
The following contingency table provides a joint frequency distribution for a group of retired
people by career and age at retirement.
848 74 38 168
10 42 94 49 195
57 179 301 186 723
Suppose one of these people is selected at random. Compute the probability that the person’s age of
retirement was between 50 and 55 given that he or she was an attorney.
85)
A)
0.140
B)
0.048
C)
0.079
D)
0.011
Provide an appropriate response.
86)
When a balanced die is rolled, the probability that the number that comes up will be a one is 1
6.
This means that if the die is rolled 36 times, a one will show up six times.
86)
A)
True
B)
False
List the outcomes comprising the specified event.
87)
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 first and last tosses are the same
List the outcomes that comprise the event (A or B).
87)
A)
HTTH, THHT
B)
HHHH, HHTH, HTHH, HTTH, THHT, THTT, TTHT, TTTT
C)
HHHH, HHTH, HHTT, HTHH, HTHT, HTTH, THHT, THTH, THTT, TTHH, TTHT, TTTT
D)
HHTT, HTHT, HTTH, THHT, THTH, TTHH
88)
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 events A and B are defined as follows.
A = event that Helen gets first prize
B = event that both prize winners are women
List the outcomes that comprise the event (A & B).
88)
A)
HJ, HG, HM
B)
HJ, HG, HM, MH
C)
HM
D)
HM, MH
Use the special multiplication rule to find the indicated probability.
89)
In a homicide case 7 different witnesses picked the same man from a lineup. The lineup contained 5
men. If the identifications were made by random guesses, find the probability that all 7 witnesses
would pick the same person.
89)
A)
1.4
B)
0.0000595
C)
0.0000128
D)
0.000064
Use the basic counting rule to solve the problem.
90)
License plates are made using 2 letters followed by 2 digits. How many plates can be made if
repetition of letters and digits is allowed?
90)
A)
456,976
B)
67,600
C)
10,000
D)
6760
Answer the question.
91)
Find the odds against correctly guessing the answer to a multiple choice question with 5 possible
answers.
91)
A)
5 to 4
B)
4 to 5
C)
5 to 1
D)
4 to 1
Describe the specified event in words.
92)
The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 4946
21–25 4808
26–30 2673
31–35 2036
36–40 612
Over 40 425
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 40 inclusive
B = event the student is over 35
Describe the event (A & B) in words.
92)
A)
The event the student is between 21 and 35 inclusive
B)
The event the student is over 40 or under 35
C)
The event the student is between 35 and 40 inclusive
D)
The event the student is over 35 but not over 40
Determine whether the events are mutually exclusive.
93)
Three board members for a nonprofit organization will be selected from a group of five people. The
board members will be selected by drawing names from a hat. The names of the five possible board
members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as
follows.
ABC ABD ABE ACD ACE
ADE BCD BCE BDE CDE
Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on
the board. The events A and B are defined as follows.
A = event that Betty and Allison are both selected
B = event that more than one man is selected
Are the events A and B mutually exclusive?
93)
A)
Yes
B)
No
Find the indicated probability.
35
94)
The Book Industry Study Group, Inc., performs sample surveys to obtain information on
characteristics of book readers. A book reader is defined to be one who read one or more books
in the six months prior to the survey; a non–book reader is defined to be one who read
newspapers or magazines but no books in the six months prior to the survey; a nonreader is
defined to be one who did not read a book, newspaper, or magazine in the six months prior to
the survey.
The following data were obtained from a random sample of people 16 years old and over.
131 150 17 298
159 141 11 311
200 98 4302
663 656 87 1406
Suppose one of these people is selected at random. Compute P( C2or I2).
94)
A)
0.107
B)
0.572
C)
0.679
D)
0.503
Use counting rules to determine the probability.
95)
Dave puts a collection of 15 books on a bookshelf in a random order. Among the books are 2 fiction
and 13 nonfiction books. What is the probability that the 2 fiction books will be all together on the
left side of the shelf and the 13 nonfiction all together on the right side of the shelf?
95)
A)
0.01333
B)
0.01619
C)
0.01809
D)
0.00952
Estimate the probability of the event.
96)
The data set represents the income levels of the members of a country club. Find the probability
that a randomly selected member earns at least $80,000. Round your answers to the nearest tenth.
96,000 112,000 74,000 120,000 77,000 96,000 80,000 68,000 136,000 176,000 71,000 88,000 128,000
77,000 112,000 104,000 80,000 144,000 65,000 104,000
96)
A)
0.4
B)
0.6
C)
0.8
D)
0.7
Draw a Venn diagram and shade the described events.
97)
From a finite sample, events A, B, and C are non–mutually exclusive. Shade the collection A and B
and C.
97)
A)
B)
C)
D)
Find the indicated probability.
98)
A committee of three people is to be formed. The three people will be selected from a list of five
possible committee members. A simple random sample of three people is taken, without
replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five
people, list the possible samples of size three and use your list to determine the probability that B is
included in the sample.
(Hint: There are 10 possible samples.)
98)
A)
7
10
B)
3
5
C)
2
5
D)
1
2
Provide an appropriate response.
99)
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, a +b + c = d?
99)
A)
True
B)
False
Solve the problem.
100)
A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many
different hands are there consisting of four hearts and one spade?
100)
A)
715
B)
13
C)
728
D)
9295
Determine the number of outcomes that comprise the specified event.
101)
The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 2175
21–25 2190
26–30 1065
31–35 899
Over 35 235
A student from the community college is selected at random. The event A is defined as follows.
A = event the student is between 26 and 35 inclusive.
Determine the number of outcomes that comprise the event (not A).
101)
A)
1964
B)
5499
C)
4600
D)
4365
Evaluate the expression.
102)
6P4
102)
A)
30
B)
2
C)
360
D)
24
Use the rule of total probability to find the indicated probability.
103)
A teacher designs a test so a student who studies will pass 95% of the time, but a student who does
not study will pass 6% of the time. A certain student studies for 93% of the tests taken. On a given
test, what is the probability that student passes?
103)
A)
0.884
B)
0.505
C)
0.888
D)
0.042
Use the basic counting rule to solve the problem.
104)
A shirt company has 3 designs each of which can be made with short or long sleeves. There are 5
color patterns available. How many different types of shirts are available from this company?
104)
A)
8
B)
30
C)
10
D)
15
List the outcome(s) of the stated event.
105)
The odds against winning in a horse race are shown in the following table.
Horse #1 #2 #3 #4 #5 #6 #7
Odds 714 321 921 3
Based on these odds, which horses comprise: A = event the winning horse’s number is above 4?
105)
A)
Horses #1, #2, #4, #5, and #6
B)
Horses #5, #6, and #7
C)
Horses #4, #5, #6, and #7
D)
Horse #7
List the outcomes comprising the specified event.
106)
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. List the outcomes that comprise the following event.
A = event exactly three tails are tossed
106)
A)
HTTT, THTT, TTHT, TTTH, TTTT
B)
HTTT, THTT, TTTH
C)
HTTT, THTT, TTHT, TTTH
D)
TTTH
Use counting rules to determine the probability.
107)
A committee of 5 members is voting on a proposal. Each member casts a yea or nay vote. On a
random voting basis, what is the probability that the final vote count is unanimous?
107)
A)
0.03125
B)
0.0625
C)
0.08333
D)
0.05
Construct the joint probability distribution corresponding to the given contingency table.
40