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 
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 
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 
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)  $\{ 2 \} , \{ \alpha \} , \{ 6 \} , \{ \pi \} , \{ 2 , \alpha \} , \{ 2,6 \} , \{ 2 , \pi \} , \{ \alpha , 6 \}$, $\{ \alpha , \pi \} , \{ 6 , \pi \} , \{ 2 , \alpha , 6 \} , \{ 2 , \alpha , \pi \} , \{ 2,6 , \pi \} , \{ \alpha , 6 , \pi \}$, $\{ 2 , \alpha , 6 , \pi \} , \varnothing$ 
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)  $\{ 1 \} , \{ 2 \} , \{ 9 \} , \{ 11 \} , \{ 1,2 \} , \{ 1,9 \} , \{ 1,11 \} , \{ 2,9 \}$,
$\{ 2,11 \} , \{ 9,11 \} , \{ 1,2,9 \} , \{ 1,2,11 \} , \{ 1,9,11 \} , \{ 2,9,11 \} , \{ 1,2,9,11 \}$ 
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 
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 
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

S = {1 Red, 1 Yellow, 1 Green, 1 Blue, 2

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 
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 
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 
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 
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 
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

S = {11 Red, 11 Yellow, 11 Green, 12 Red

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 
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 
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 
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)  $\frac { 1 } { 18 }$ 
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 
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 
A)  0.47 
B)  0.67 
C)  0.37 
D)  0.57

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. -In a survey about the number of siblings of college students, the following probability table was constructed: Number of Siblings Probability 0 0.27 1 0.31 2 0.20 3 0.13 4 or more 0.09 What is the probability that a student has at most 2 siblings?

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. -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) $\frac { 17 } { 18 }$ C) 2 D) $\frac { 1 } { 18 }$

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

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

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Exam 12: Counting and Probability