Question 1

Find the value of the permutation.
-P(3, 3)

Accepted Answer

A)  6 
B)  2 
C)  1 
D)  3

Question 2

Choose the one alternative that best completes the statement or answers the question.
-The psychology lab at a college is staffed by 9 male doctoral students, 8 female doctoral students, 16 male undergraduates, and 6 female undergraduates. If a person is selected at random from the group, find the
Probability that the selected person is an undergraduate or a female.

Accepted Answer

A)  $\frac { 10 } { 13 }$ 
B)  $\frac { 14 } { 39 }$ 
C)  $\frac { 22 } { 39 }$ 
D)  $\frac { 8 } { 13 }$

Question 3

Solve the problem.
-From 9 names on a ballot, a committee of 5 will be elected to attend a political national convention. How many different committees are possible?

Accepted Answer

A)  3,024 
B)  15,120 
C)  7,560 
D)  126

Question 4

Solve the problem.
-How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed.

Accepted Answer

A)  9,000 
B)  3,024 
C)  6,561 
D)  6,480

Question 5

Find the value of the combination.
-C(7, 7)

Accepted Answer

A)  1,260 
B)  1 
C)  0.5 
D)  5,040

Question 6

Choose the one alternative that best completes the statement or answers the question.
-The table below shows the results of a consumer survey of annual incomes in 100 households. $$\begin{array} { l | c } 
\text { Income } & \text { Number of households } \
\hline \$ 0 - 14,999 & 9 \
\hline \$ 15,000 - 24,999 & 25 \
\hline \$ 25,000 - 34,999 & 27 \
\hline \$ 35,000 - 44,999 & 25 \
\hline \$ 45,000 \text { or more } & 14
\end{array}$$ What is the probability that a household has an annual income between $15,000 and $44,999 inclusive?

Accepted Answer

A)  0.52 
B)  0.5 
C)  0.77 
D)  0.27

Question 7

Solve the problem.
-In survey of 50 households, 25 responded that they have an HDTV television, 35 responded that they had a multimedia personal computer and 15 responded they had both. How many households had neither an HDTV
Television nor a multimedia personal computer?

Accepted Answer

A)  25 
B)  15 
C)  5 
D)  35

Question 8

Solve the problem.
-List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is C(4, 3)?

Accepted Answer

A)  123, 124, 134, 234, 321, 432 C(4, 3) = 6 
B)  111, 112, 113, 114, 121, 122, 123, 124, 131, 132, 133, 134, 141, 142, 143, 144, 211, 212, 213, 214, 221, 222, 223, 224, 231, 232, 233, 234, 241, 242, 243, 244, 311, 312, 313, 314, 321, 322, 323, 324, 331, 332, 333, 334, 341, 342, 343, 344, 411, 412,
413, 414, 421, 422, 423, 424, 431, 432, 433, 434, 441, 442, 443, 444
C(4, 3) = 64 
C)  123, 124, 134, 234 C(4, 3) = 4 
D)  123, 124, 132, 134, 142, 143, 213, 214, 231, 234, 241, 243, 312, 314, 321, 324, 341, 342, 412, 413, 421, 423, 431, 432 C(4, 3) = 24

Question 9

Solve the problem.
-A survey of 2,504 credit card users indicated that 1,167 had bought books online, 1,226 had bought music online, 431 had bought pet supplies online, 128 had bought both books and music, 227 had bought both books and pet
Supplies, 198 had bought both music and pet supplies, and 99 had bought all three. How many credit card users
Did not buy any of the three? How many bought either books or pet supplies but not music?

Accepted Answer

A)  233; 1,016 
B)  134; 1,115 
C)  134; 1,144 
D)  134; 1,016

Question 10

Use the information given in the figure.
-
How many are in set A?

Accepted Answer

A)  37 
B)  35 
C)  30 
D)  34

Question 11

Solve the problem.
-A man has 10 shirts and 9 ties. How many different shirt and tie arrangements can he wear?

Accepted Answer

A)  180 
B)  90 
C)  100 
D)  81

Question 12

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
-Rolling a 6-sided fair die once

Accepted Answer

The answer of Write the word or phrase that best...

Question 13

Choose the one alternative that best completes the statement or answers the question.
-The table below shows the results of a consumer survey of annual incomes in 100 households. $$\begin{array} { l | c } 
\text { Income } & \text { Number of households } \
\hline \$ 0 - 14,999 & 7 \
\hline \$ 15,000 - 24,999 & 20 \
\hline \$ 25,000 - 34,999 & 30 \
\hline \$ 35,000 - 44,999 & 26 \
\hline \$ 45,000 \text { or more } & 17
\end{array}$$ What is the probability that a household has an annual income less than $25,000?

Accepted Answer

A)  0.57 
B)  0.2 
C)  0.27 
D)  0.73

Question 14

Choose the one alternative that best completes the statement or answers the question.
-In a survey about the number of siblings of college students, the following probability table was constructed: $$\begin{array} { c | c } 
\text { Number of Siblings } & \text { Probability } \
\hline 0 & 0.25 \
\hline 1 & 0.34 \
\hline 2 & 0.21 \
\hline 3 & 0.09 \
\hline 4 \text { or more } & 0.11
\end{array}$$ What is the probability that a student 3 or more siblings?

Accepted Answer

A)  0.09 
B)  0.11 
C)  0.2 
D)  0.8

Question 15

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
-Tossing one fair coin three times

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Choose the one alternative that best completes the statement or answers the question.
-Sam estimates that if he leaves his car parked outside his office all day on a weekday, the chance that he will get a parking ticket is 22%. If Sam leaves his car parked outside his office all day next Tuesday, what is the chance
That he will not get a parking ticket?

Accepted Answer

A)  4.84% 
B)  22% 
C)  78% 
D)  -22%

Question 17

Choose the one alternative that best completes the statement or answers the question.
-A spinner has regions numbered 1 through 21. What is the probability that the spinner will stop on an even number or a multiple of 3?

Accepted Answer

A)  $\frac { 10 } { 9 }$ 
B)  17 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { 1 } { 3 }$

Question 18

Use the information given in the figure.
-
How many are in B or $C$ ?

Accepted Answer

A)  6 
B)  51 
C)  42 
D)  50

Question 19

Solve the problem.
-In a survey of 189 vacationers in a popular beach resort town, 73 indicated they would consider buying a home there, 73 would consider buying a beach villa, 59 would consider buying a lot, 24 would consider both a home
And a villa, 27 would consider both a home and a lot, 26 would consider both a villa and a lot, and 12 would
Consider all three. How many vacationers would not consider any of the three? How many would consider only
A home?

Accepted Answer

A)  49; 18 
B)  49; 35 
C)  61; 46 
D)  49; 34

Question 20

Solve the problem.
-An exam consists of 9 multiple-choice questions and 6 essay questions. If the student must answer 5 of the multiple-choice questions and 3 of the essay questions, in how many ways can the questions be chosen?

Accepted Answer

A)  810 
B)  2520 
C)  1,814,400 
D)  261,273,600

Exam 12: Counting and Probability

Find the value of the permutation. -P(3, 3)

Solve the problem. -From 9 names on a ballot, a committee of 5 will be elected to attend a political national convention. How many different committees are possible?

Solve the problem. -How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digit cannot be 0? Repeated digits are allowed.

Find the value of the combination. -C(7, 7)

Solve the problem. -In survey of 50 households, 25 responded that they have an HDTV television, 35 responded that they had a multimedia personal computer and 15 responded they had both. How many households had neither an HDTV Television nor a multimedia personal computer?

Solve the problem. -List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is C(4, 3) ?

Use the information given in the figure. - How many are in set A?

Solve the problem. -A man has 10 shirts and 9 ties. How many different shirt and tie arrangements can he wear?

Write the word or phrase that best completes each statement or answers the question. Construct a probability model for the experiment. -Rolling a 6-sided fair die once

Write the word or phrase that best completes each statement or answers the question. Construct a probability model for the experiment. -Tossing one fair coin three times

Choose the one alternative that best completes the statement or answers the question. -A spinner has regions numbered 1 through 21. What is the probability that the spinner will stop on an even number or a multiple of 3?

Use the information given in the figure. - How many are in B or $C$ ?

Solve the problem. -An exam consists of 9 multiple-choice questions and 6 essay questions. If the student must answer 5 of the multiple-choice questions and 3 of the essay questions, in how many ways can the questions be chosen?