Question 1

Solve the problem.
-How many different license plates can be made using 3 letters followed by 4 digits selected from the digits 0 through 9, if digits may be repeated but letters may not be repeated?

Accepted Answer

A)   175,760,000
B)   88,583,040
C)   156,000,000
D)   216,666.667 C

Question 2

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: $$\begin{array} { c | c } 
\text { Number of Siblings } & \text { Probability } \
\hline 0 & 0.23 \
\hline 1 & 0.34 \
\hline 2 & 0.17 \
\hline 3 & 0.12 \
\hline 4 \text { or more } & 0.14
\end{array}$$ What is the probability that a student has 1, 2, or 3 siblings?

Accepted Answer

A)   0.51
B)   0.63
C)   0.86
D)   0.29  B

Question 3

Choose the one alternative that best completes the statement or answers the question.
-A bag contains 13 balls numbered 1 through 13. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Accepted Answer

A)    136\frac { 13 } { 6 }613​ 
B)   6
C)    613\frac { 6 } { 13 }136​ 
D)    213\frac { 2 } { 13 }132​ C

Question 4

Write down all the subsets of the given set.
-$\{ p , q , r \}$

Accepted Answer

A)    {p},{q},{r},{p,q},{p,r},{q,r},{p,q,r}\{ p \} , \{ q \} , \{ r \} , \{ p , q \} , \{ p , r \} , \{ q , r \} , \{ p , q , r \}{p},{q},{r},{p,q},{p,r},{q,r},{p,q,r} 
B)    ∅,{p},{q},{r},{p,q},{p,r},{q,r},{p,p},{q,q},{r,r},{p,q,r}\varnothing , \{ p \} , \{ q \} , \{ r \} , \{ p , q \} , \{ p , r \} , \{ q , r \} , \{ p , p \} , \{ q , q \} , \{ r , r \} , \{ p , q , r \}∅,{p},{q},{r},{p,q},{p,r},{q,r},{p,p},{q,q},{r,r},{p,q,r} 
C)    ∅,{p},{q},{r},{p,q},{p,r},{q,r}\varnothing , \{ p \} , \{ q \} , \{ r \} , \{ p , q \} , \{ p , r \} , \{ q , r \}∅,{p},{q},{r},{p,q},{p,r},{q,r} 
D)    ∅,{p},{q},{r},{p,q},{p,r},{q,r},{p,q,r}\varnothing , \{ p \} , \{ q \} , \{ r \} , \{ p , q \} , \{ p , r \} , \{ q , r \} , \{ p , q , r \}∅,{p},{q},{r},{p,q},{p,r},{q,r},{p,q,r}

Question 5

Solve the problem.
-A restaurant offers a choice of 5 salads, 7 main courses, and 3 desserts. How many possible 3-course meals are there?

Accepted Answer

A)   210 possible meals
B)   105 possible meals
C)   35 possible meals
D)   15 possible meals

Question 6

Solve the problem.
-If $n ( A ) = 25 , n ( A \cup B ) = 73$, and $n ( A \cap B ) = 21$, find $n ( B )$.

Accepted Answer

A)   69
B)   68
C)   48
D)   70

Question 7

Write down all the subsets of the given set.
-$\{ 1,2,9,11 \}$

Accepted Answer

A)    {1},{2},{9},{11},{1,2},{1,9},{1,11},{2,9}\{ 1 \} , \{ 2 \} , \{ 9 \} , \{ 11 \} , \{ 1,2 \} , \{ 1,9 \} , \{ 1,11 \} , \{ 2,9 \}{1},{2},{9},{11},{1,2},{1,9},{1,11},{2,9} , {2,11},{9,11},{1,2,9},{1,2,11},{1,9,11},{2,9,11},{1,2,9,11},∅\{ 2,11 \} , \{ 9,11 \} , \{ 1,2,9 \} , \{ 1,2,11 \} , \{ 1,9,11 \} , \{ 2,9,11 \} , \{ 1,2,9,11 \} , \varnothing{2,11},{9,11},{1,2,9},{1,2,11},{1,9,11},{2,9,11},{1,2,9,11},∅ 
B)    {2},{5},{6},{7},{2,5},{2,6},{2,7},{5,6}\{ 2 \} , \{ 5 \} , \{ 6 \} , \{ 7 \} , \{ 2,5 \} , \{ 2,6 \} , \{ 2,7 \} , \{ 5,6 \}{2},{5},{6},{7},{2,5},{2,6},{2,7},{5,6} , {5,7},{6,7},{2,5,6},{2,5,7},{2,6,7}\{ 5,7 \} , \{ 6,7 \} , \{ 2,5,6 \} , \{ 2,5,7 \} , \{ 2,6,7 \}{5,7},{6,7},{2,5,6},{2,5,7},{2,6,7} , {5,6,7},∅\{ 5,6,7 \} , \varnothing{5,6,7},∅ 
C)    {1},{2},{9},{11},{1,2},{1,9},{1,11},{2,9}\{ 1 \} , \{ 2 \} , \{ 9 \} , \{ 11 \} , \{ 1,2 \} , \{ 1,9 \} , \{ 1,11 \} , \{ 2,9 \}{1},{2},{9},{11},{1,2},{1,9},{1,11},{2,9} , {2,11},{1,2,9},{1,2,11},{1,9,11},{2,9,11}\{ 2,11 \} , \{ 1,2,9 \} , \{ 1,2,11 \} , \{ 1,9,11 \} , \{ 2,9,11 \}{2,11},{1,2,9},{1,2,11},{1,9,11},{2,9,11} , {1,2,9,11},∅\{ 1,2,9,11 \} , \varnothing{1,2,9,11},∅ 
D)    {1},{2},{9},{11},{1,2},{1,9},{1,11},{2,9}\{ 1 \} , \{ 2 \} , \{ 9 \} , \{ 11 \} , \{ 1,2 \} , \{ 1,9 \} , \{ 1,11 \} , \{ 2,9 \}{1},{2},{9},{11},{1,2},{1,9},{1,11},{2,9} , {2,11},{9,11},{1,2,9},{1,2,11},{1,9,11},{2,9,11},{1,2,9,11}\{ 2,11 \} , \{ 9,11 \} , \{ 1,2,9 \} , \{ 1,2,11 \} , \{ 1,9,11 \} , \{ 2,9,11 \} , \{ 1,2,9,11 \}{2,11},{9,11},{1,2,9},{1,2,11},{1,9,11},{2,9,11},{1,2,9,11}

Question 8

Choose the one alternative that best completes the statement or answers the question.
-Suppose that the sample space is $S = \{ 1,2,3,4,5,6,7,8,9,10 \rangle$ and that outcomes are equally likely. Compute the probability of the event $E = \{ 2,10 \}$.

Accepted Answer

A)   2
B)    15\frac { 1 } { 5 }51​ 
C)    110\frac { 1 } { 10 }101​ 
D)    29\frac { 2 } { 9 }92​

Question 9

Use the information given in the figure.
-
How many are in B but not in A?

Accepted Answer

A)   25
B)   27
C)   20
D)   15

Question 10

Determine whether the following is a probability model.
-$\begin{array}{l|c}
\text { Outcome } & \text { Probability } \
\hline \text { Jim } & 0 \
\text { Tom } & 0 \
\text { Bill } & 1 \
\text { Carl } & 0
\end{array}$

Accepted Answer

A)   Yes
B)   No

Question 11

Solve the problem.
-How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 6 forwards, 7 midfield players, and 5 defensive players?

Accepted Answer

A)   6,048,000
B)   7,000
C)   65
D)   43,758

Question 12

Choose the one alternative that best completes the statement or answers the question.
-Find the probability of getting 2 tails when 3 fair coins are tossed.

Accepted Answer

A)    23\frac { 2 } { 3 }32​ 
B)    12\frac { 1 } { 2 }21​ 
C)    14\frac { 1 } { 4 }41​ 
D)    38\frac { 3 } { 8 }83​

Question 13

Solve the problem.
-How many different 8-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used and no letter can be used more than once?

Accepted Answer

A)   4,782,969
B)   36
C)   7
D)   181,440

Question 14

Write the word or phrase that best completes each statement or answers the question.
Construct a probability model for the experiment.
-Spinner I has 3 sections of equal area, numbered 1, 2, and 3. Spinner II has 3 sections of equal area, labeled Red, Yellow,
and Green. Spin Spinner I twice, then Spinner II.
What is the probability of getting a 2, followed by a 1, followed by Yellow or Red?

Accepted Answer

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

Question 15

Determine whether the following is a probability model.
-$\begin{array}{l|c}
\text { Outcome } & \text { Probability } \
\hline \text { Red } & 0.16 \
\text { Blue } & 0.17 \
\text { Green } & 0.25 \
\text { White } & 0.27
\end{array}$

Accepted Answer

A)   Yes
B)    No\mathrm { No }No

Question 16

Choose the one alternative that best completes the statement or answers the question.
-Suppose that the sample space is $\mathrm { S } = \{ 1,2,3,4,5,6,7,8,9,10 \}$ and that outcomes are equally likely. Compute the probability of the event $E = \{ 1,2,4,5,7,9,10 \}$.

Accepted Answer

A)   7
B)    710\frac { 7 } { 10 }107​ 
C)    79\frac { 7 } { 9 }97​ 
D)    45\frac { 4 } { 5 }54​

Question 17

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 twice

Accepted Answer

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

Question 18

Solve the problem.
-A committee is to be formed consisting of 2 men and 3 women. If the committee members are to be chosen from 13 men and 9 women, how many different committees are possible?

Accepted Answer

A)   6,552
B)   78,624
C)   26,334
D)   162

Question 19

Find the value of the combination.
-C(5, 1)

Accepted Answer

A)   48
B)   5
C)   120
D)   2.5

Question 20

Solve the problem.
-How many different 11-letter words (real or imaginary) can be formed from the letters in the word ENGINEERING?

Accepted Answer

A)   39,916,800
B)   554,400
C)   25,200
D)   277,200

Exam 12: Counting and Probability

Solve the problem. -How many different license plates can be made using 3 letters followed by 4 digits selected from the digits 0 through 9, if digits may be repeated but letters may not be repeated?

Choose the one alternative that best completes the statement or answers the question. -A bag contains 13 balls numbered 1 through 13. What is the probability of selecting a ball that has an even number when one ball is drawn from the bag?

Write down all the subsets of the given set. - $\{ p , q , r \}$

Solve the problem. -A restaurant offers a choice of 5 salads, 7 main courses, and 3 desserts. How many possible 3-course meals are there?

Solve the problem. -If $n ( A ) = 25 , n ( A \cup B ) = 73$ , and $n ( A \cap B ) = 21$ , find $n ( B )$ .

Write down all the subsets of the given set. - $\{ 1,2,9,11 \}$

Choose the one alternative that best completes the statement or answers the question. -Suppose that the sample space is $S = \{ 1,2,3,4,5,6,7,8,9,10 \rangle$ and that outcomes are equally likely. Compute the probability of the event $E = \{ 2,10 \}$ .

Use the information given in the figure. - How many are in B but not in A?

Determine whether the following is a probability model. - $\begin{array}{l|c}\text { Outcome } & \text { Probability } \\\hline \text { Jim } & 0 \\\text { Tom } & 0 \\\text { Bill } & 1 \\\text { Carl } & 0\end{array}$

Solve the problem. -How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 6 forwards, 7 midfield players, and 5 defensive players?

Choose the one alternative that best completes the statement or answers the question. -Find the probability of getting 2 tails when 3 fair coins are tossed.

Solve the problem. -How many different 8-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used and no letter can be used more than once?

Determine whether the following is a probability model. - $\begin{array}{l|c}\text { Outcome } & \text { Probability } \\\hline \text { Red } & 0.16 \\\text { Blue } & 0.17 \\\text { Green } & 0.25 \\\text { White } & 0.27\end{array}$

Choose the one alternative that best completes the statement or answers the question. -Suppose that the sample space is $\mathrm { S } = \{ 1,2,3,4,5,6,7,8,9,10 \}$ and that outcomes are equally likely. Compute the probability of the event $E = \{ 1,2,4,5,7,9,10 \}$ .

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 twice

Solve the problem. -A committee is to be formed consisting of 2 men and 3 women. If the committee members are to be chosen from 13 men and 9 women, how many different committees are possible?

Find the value of the combination. -C(5, 1)

Solve the problem. -How many different 11-letter words (real or imaginary) can be formed from the letters in the word ENGINEERING?