Question 1

Solve the problem.
-What is the probability that at least 2 people have the same birth month in a group of 4 people?

Accepted Answer

A)  0.573 
B)  0.456 
C)  0.544 
D)  0.427

Question 2

Solve the problem.
-In a survey about the number of siblings of college students, the following probability table was constructed: $$\begin{array} { c | c } 
\text { Number of Siblings } & \text { Probability } \
\hline 0 & 0.27 \
\hline 1 & 0.31 \
\hline 2 & 0.20 \
\hline 3 & 0.13 \
\hline 4 \text { or more } & 0.09
\end{array}$$ What is the probability that a student has at most 2 siblings?

Accepted Answer

A)  0.58 
B)  0.42 
C)  0.78 
D)  0.22

Question 3

Solve the problem.
-List all the ordered arrangements of 6 objects a, b, c, d, e, and f choosing 2 at a time without repetition. What is P(6, 2)?

Accepted Answer

A)  ab, ac, ad, ae, af, bc, bd, be, bf, cd, ce, cf, de, df, ef P(6, 2) = 15 
B)  ab, ac, ad, ae, af, ba, bc, bd, be, bf, ca, cb, cd, ce, cf, da, db, dc, de, df, ea, eb, ec, ed, ef, fa, fb, fc, fd, fe P(6, 2) = 30 
C)  ab, ac, ad, ae, af, ba, bc, bd, be, bf, ca, cb, cd, ce, cf, da, db, dc, de, df, ea, eb, ec, ed, ef P(6, 2) = 25 
D)  aa, ab, ac, ad, ae, af, ba, bb, bc, bd, be, bf, ca, cb, cc, cd, ce, cf, da, db, dc, dd, de, df, ea, eb, ec, ed, ee, ef, fa, fb, fc, fd, fe, ff
P(6, 2) = 36

Question 4

Write down all the subsets of the given set.
-$\{ 2 , \alpha , 6 , \pi \}$

Accepted Answer

A)  $\{ 2 \} , \{ \alpha \} , \{ 6 \} , \{ \pi \} , \{ 2 , \alpha \} , \{ 2,6 \} , \{ 2 , \pi \} , \{ \alpha , 6 \}$, $\{ \alpha , \pi \} , \{ 6 , \pi \} , \{ 2 , \alpha , 6 \} , \{ 2 , \alpha , \pi \} , \{ 2,6 , \pi \} , \{ \alpha , 6 , \pi \} , \varnothing$ 
B)  $\{ 2 \} , \{ \alpha \} , \{ 6 \} , \{ \pi \} , \{ 2 , \alpha \} , \{ 2,6 \} , \{ 2 , \pi \} , \{ \alpha , 6 \}$, $\{ \alpha , \pi \} , \{ 6 , \pi \} , \{ 2 , \alpha , \pi \} , \{ 2,6 , \pi \} , \{ \alpha , 6 , \pi \}$, $\{ 2 , \alpha , 6 , \pi \} , \varnothing$ 
C)  $\{ 2 \} , \{ \alpha \} , \{ 6 \} , \{ \pi \} , \{ 2 , \alpha \} , \{ 2,6 \} , \{ 2 , \pi \} , \{ \alpha , 6 \}$, $\{ \alpha , \pi \} , \{ 6 , \pi \} , \{ 2 , \alpha , 6 \} , \{ 2 , \alpha , \pi \} , \{ 2,6 , \pi \} , \{ \alpha , 6 , \pi \}$, $\{ 2 , \alpha , 6 , \pi \}$ 
D)  $\{ 2 \} , \{ \alpha \} , \{ 6 \} , \{ \pi \} , \{ 2 , \alpha \} , \{ 2,6 \} , \{ 2 , \pi \} , \{ \alpha , 6 \}$, $\{ \alpha , \pi \} , \{ 6 , \pi \} , \{ 2 , \alpha , 6 \} , \{ 2 , \alpha , \pi \} , \{ 2,6 , \pi \} , \{ \alpha , 6 , \pi \}$, $\{ 2 , \alpha , 6 , \pi \} , \varnothing$

Question 5

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

Accepted Answer

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

Question 6

Solve the problem.
-During July in Jacksonville, Florida, it is not uncommon to have afternoon thunderstorms. On average, 9.5 days have afternoon thunderstorms. What is the probability that a randomly selected day in July will not have a
Thunderstorm? Round to two decimal places, if necessary.

Accepted Answer

A)  0.91 
B)  0.68 
C)  0.31 
D)  0.69

Question 7

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

Question 8

onstruct a probability model for the experiment.
-Spinner I has 4 sections of equal area, numbered 1, 2, 3, and 4, and Spinner II has 4 sections of equal area, labeled Red,
Yellow, Green, and Blue. Spin Spinner I and then spin Spinner II.
What is the probability of getting a 1 or 3 followed by Red?

Accepted Answer

The answer of onstruct a probability model for the experiment.
-Spinner...

Question 9

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

Accepted Answer

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

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.
-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 12

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 13

Find the value of the permutation.
-P(9, 1)

Accepted Answer

A)  362,880 
B)  1 
C)  40,320 
D)  9

Question 14

onstruct 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 onstruct a probability model for the experiment.
-Spinner...

Question 15

Solve the problem.
-In a survey of 421 computer buyers, 213 put price as a main consideration, 205 put performance as a main consideration, and 57 listed both price and performance. How many computer buyers listed other
Considerations? How many looked only for performance?

Accepted Answer

A)  117; 205 
B)  156; 148 
C)  60; 205 
D)  60; 148

Question 16

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 17

Solve the problem.
-$$\text { If } n ( A ) = 37 , n ( B ) = 52 \text {, and } n ( A \cup B ) = 70 \text {, find } n ( A \cap B )$$

Accepted Answer

A)  89 
B)  51 
C)  19 
D)  38

Question 18

Solve the problem.
-Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be 3? A) $\frac { 1 } { 2 }$

В) $\frac { 17 } { 18 }$

Accepted Answer

C)  2 
D)  $\frac { 1 } { 18 }$

Question 19

Solve the problem.
-How many different vertical arrangements are there of 8 flags if 3 are white, 3 are blue, and 2 are red?

Accepted Answer

A)  560 
B)  18 
C)  56 
D)  21

Question 20

Solve the problem.
-$$\text { Given that } P ( A ) = 0.15 , P ( B ) = 0.42 \text {, and } P ( A \cap B ) = 0.10 \text {, find } P ( A \cup B ) \text {. }$$

Accepted Answer

A)  0.47 
B)  0.67 
C)  0.37 
D)  0.57

Exam 12: Counting and Probability

Solve the problem. -What is the probability that at least 2 people have the same birth month in a group of 4 people?

Solve the problem. -List all the ordered arrangements of 6 objects a, b, c, d, e, and f choosing 2 at a time without repetition. What is P(6, 2) ?

Write down all the subsets of the given set. - $\{ 2 , \alpha , 6 , \pi \}$

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

Solve the problem. -During July in Jacksonville, Florida, it is not uncommon to have afternoon thunderstorms. On average, 9.5 days have afternoon thunderstorms. What is the probability that a randomly selected day in July will not have a Thunderstorm? Round to two decimal places, if necessary.

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?

onstruct a probability model for the experiment. -Spinner I has 4 sections of equal area, numbered 1, 2, 3, and 4, and Spinner II has 4 sections of equal area, labeled Red, Yellow, Green, and Blue. Spin Spinner I and then spin Spinner II. What is the probability of getting a 1 or 3 followed by Red?

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

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

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

Find the value of the permutation. -P(9, 1)

Solve the problem. -In a survey of 421 computer buyers, 213 put price as a main consideration, 205 put performance as a main consideration, and 57 listed both price and performance. How many computer buyers listed other Considerations? How many looked only for performance?

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.

Solve the problem. - $\text { If } n ( A ) = 37 , n ( B ) = 52 \text {, and } n ( A \cup B ) = 70 \text {, find } n ( A \cap B )$

Solve the problem. -How many different vertical arrangements are there of 8 flags if 3 are white, 3 are blue, and 2 are red?

Solve the problem. - $\text { Given that } P ( A ) = 0.15 , P ( B ) = 0.42 \text {, and } P ( A \cap B ) = 0.10 \text {, find } P ( A \cup B ) \text {. }$