Question 1

Tell whether the statement is true or false.
-$\{4,8,13\}=\{0,4,8,13\}$

Accepted Answer

A) True 
 B)False

Question 2

Find the probability.
-A calculator requires a keystroke assembly and a logic circuit. Assume that $80 \%$ of the keystroke assemblies and $81 \%$ of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory.

Accepted Answer

A)  .6561 
B)  .8100 
C)  .6480 
D)  .6400 
A)  .6561 
B)  .8100 
C)  .6480 
D)  .6400

Question 3

Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has twodominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and"hybrid" describes one who has one of each.
-Two hybrids produce a litter of four offspring. What is the probability that exactly one is pure recessive?

Accepted Answer

A)  .25 
B)  .422 
C)  .211 
D) .133 
A)  .25 
B)  .422 
C)  .211 
D) .133

Question 4

Use the given table to find the indicated probability.
-People were given three choices of soft drinks and asked to choose one favorite. The following table shows the results.
 
$\mathrm{P}($ person is over 40 | person drinks root beer)?

Accepted Answer

A)  $\frac{6}{17}$ 
B)  $\frac{2}{5}$ 
C)  $\frac{5}{17}$ 
D)  None of the above 
A)  $\frac{6}{17}$ 
B)  $\frac{2}{5}$ 
C)  $\frac{5}{17}$ 
D)  None of the above

Question 5

Use a Venn diagram to decide if the statement is true or false.
-$\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)^{\prime}=\mathrm{A} \cap \mathrm{B}^{\prime}$

Accepted Answer

A) True 
 B)False

Question 6

Decide whether the statement is true or false.
-$\{15,14,7\} \cap \varnothing=\{15,14,7\}$

Accepted Answer

A) True 
 B)False

Question 7

Write the word or phrase that best completes each statement or answers thequestion.
-If $P(A)=P(A \mid B)$, why must $P(B)=P(B \mid A)$ ?

Accepted Answer

P(A) = P(A|B) implie

Question 8

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$, and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.
-$\mathrm{A}^{\prime} \cap \mathrm{K}^{\prime}$

Accepted Answer

A)  $\{n\}$ 
B)  $\{\mathrm{c}, \mathrm{p}, \mathrm{r}, \mathrm{t}\}$ 
C)  $\{\mathrm{c}, \mathrm{n}, \mathrm{p}, \mathrm{r}, \mathrm{t}\}$ 
D)  $\varnothing$ 
A)  $\{n\}$ 
B)  $\{\mathrm{c}, \mathrm{p}, \mathrm{r}, \mathrm{t}\}$ 
C)  $\{\mathrm{c}, \mathrm{n}, \mathrm{p}, \mathrm{r}, \mathrm{t}\}$ 
D)  $\varnothing$

Question 9

A die is rolled twice. Write the indicated event in set notation.
-The first roll is a 2 and so is the second.

Accepted Answer

A)  $\{(2,2)\}$ 
B)  $\{(2,2),(1,2),(2,1),(2,5),(5,2)\}$ 
C)  $(1,2),(2,2),(3,2),(4,2),(5,2),(6,2)\}$ 
D)  $\{(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\}$ 
A)  $\{(2,2)\}$ 
B)  $\{(2,2),(1,2),(2,1),(2,5),(5,2)\}$ 
C)  $(1,2),(2,2),(3,2),(4,2),(5,2),(6,2)\}$ 
D)  $\{(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\}$

Question 10

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$. List the members of the indicated set, using set braces.
-$\mathrm{A} \cup(\mathrm{B} \cap \mathrm{C})$

Accepted Answer

A)  $\{q, y, z\}$ 
B)  $\{q, w, y\}$ 
C)  $\{q, r, w, y, z\}$ 
D)  $\{q, s, u, w, y, z\}$ 
A)  $\{q, y, z\}$ 
B)  $\{q, w, y\}$ 
C)  $\{q, r, w, y, z\}$ 
D)  $\{q, s, u, w, y, z\}$

Question 11

Find the odds in favor of the indicated event.
-Randomly drawing a 4 from the cards pictured below.

Accepted Answer

A)  5 to 1 
B)  1 to 5 
C)  1 to 4 
D)  4 to 1 
A)  5 to 1 
B)  1 to 5 
C)  1 to 4 
D)  4 to 1

Question 12

Use the given table to find the indicated probability.
-The following table contains data from a study of two airlines which fly to Smalltown, USA.
 
P(flight arrived on time $n$ flight was on Upstate Airlines)?

Accepted Answer

A)  $\frac{11}{76}$ 
B)  $\frac{43}{87}$ 
C)  $\frac{43}{76}$ 
D)  None of the above 
A)  $\frac{11}{76}$ 
B)  $\frac{43}{87}$ 
C)  $\frac{43}{76}$ 
D)  None of the above

Question 13

Decide whether the two events listed are independent.
-A fair die is rolled twice. F is the event that six appears on the first roll and $S$ is the event that six appears on the second roll.

Accepted Answer

A) True 
 B)False

Question 14

Find the odds in favor of the indicated event.
-Rolling a 4 with a fair die.

Accepted Answer

A)  1 to 4 
B)  2 to 3 
C)  1 to 6 
D)  1 to 5 
A)  1 to 4 
B)  2 to 3 
C)  1 to 6 
D)  1 to 5

Question 15

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$, and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.
-$\mathrm{L} \cap \mathrm{K}$

Accepted Answer

A)  $\{\mathrm{c}, \mathrm{n}, \mathrm{r}, \mathrm{s}, \mathrm{t}\}$ 
B)  $\{c, h, n, w\}$ 
C)  $\{\mathrm{r}, \mathrm{s}, \mathrm{t}\}$ 
D)  $\{c, h, n, r, s, t, w\}$ 
A)  $\{\mathrm{c}, \mathrm{n}, \mathrm{r}, \mathrm{s}, \mathrm{t}\}$ 
B)  $\{c, h, n, w\}$ 
C)  $\{\mathrm{r}, \mathrm{s}, \mathrm{t}\}$ 
D)  $\{c, h, n, r, s, t, w\}$

Question 16

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.
-$\mathrm{n}(\mathrm{U})=235, \mathrm{n}(\mathrm{A})=80, \mathrm{n}(\mathrm{B})=100, \mathrm{n}(\mathrm{A} \cap \mathrm{B}) \quad=35, \mathrm{n}(\mathrm{A} \cap \mathrm{C})=38, \mathrm{n}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=18$, $n\left(A^{\prime} \cap B \cap C^{\prime}\right)=47$, and $n\left(A^{\prime} \cap B^{\prime} \cap C^{\prime}\right)=60$. Find $n(C)$.

Accepted Answer

A)  50 
B)  46 
C)  86 
D)  30 
A)  50 
B)  46 
C)  86 
D)  30

Question 17

Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has twodominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and"hybrid" describes one who has one of each.
-In a population, $50 \%$ of females are pure dominant, $40 \%$ are hybrid, and $10 \%$ are pure recessive. If a pure recessive male mates with a random female and their first offspring has the dominant trait, what is the probability that the female is pure dominant?

Accepted Answer

A)  .50 
B)  .75 
C)  .56 
D)  .34 
A)  .50 
B)  .75 
C)  .56 
D)  .34

Question 18

The table shows, for some particular year, a listing of several income levels and, for each level, the proportion of the population in the level and the probability that a person in that level bought a new car during the year. Given that one of the people who bought a new car during that year is randomly selected, find the probability that that person was in the indicated income category. Round your answer to the nearest hundredth.
  
-$\$ 0$ - $\$ 4999$

Accepted Answer

A)  .05 
B)  .01 
C)  .03 
D) .02 
A)  .05 
B)  .01 
C)  .03 
D) .02

Question 19

Write the word or phrase that best completes each statement or answers the question.
-Assume that the events $A_{1}, A_{2}, \ldots, A_{n}$ are mutually exclusive events whose union is the sample space, and that $B$ is an event that has occurred. Use Bayes' theorem to write an equation for $\mathrm{P}\left(\mathrm{A}_{1} \mid \mathrm{B}\right)$.

Accepted Answer

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

Question 20

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.
-$\mathrm{n}(\mathrm{A} \cup \mathrm{B} \cup \mathrm{C})=157, \mathrm{n}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=21, \mathrm{n}(\mathrm{A} \cap \mathrm{B})=44, \mathrm{n}(\mathrm{A} \cap \mathrm{C})=41, \mathrm{n}(\mathrm{B} \cap \mathrm{C})=39, \mathrm{n}(\mathrm{A})=106$, $n(B)=78$, and $n(C)=76$. Find $n\left(A^{\prime} \cap B \cap C\right)$

Accepted Answer

A)  20 
B)  19 
C)  17 
D)  18 
A)  20 
B)  19 
C)  17 
D)  18

Tell whether the statement is true or false. - $\{4,8,13\}=\{0,4,8,13\}$

Find the probability. -A calculator requires a keystroke assembly and a logic circuit. Assume that $80 \%$ of the keystroke assemblies and $81 \%$ of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory.

Decide whether the statement is true or false. - $\{15,14,7\} \cap \varnothing=\{15,14,7\}$

Write the word or phrase that best completes each statement or answers thequestion. -If $P(A)=P(A \mid B)$ , why must $P(B)=P(B \mid A)$ ?

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set. - $\mathrm{A}^{\prime} \cap \mathrm{K}^{\prime}$

A die is rolled twice. Write the indicated event in set notation. -The first roll is a 2 and so is the second.

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces. - $\mathrm{A} \cup(\mathrm{B} \cap \mathrm{C})$

Find the odds in favor of the indicated event. -Randomly drawing a 4 from the cards pictured below.

Use the given table to find the indicated probability. -The following table contains data from a study of two airlines which fly to Smalltown, USA. P(flight arrived on time $n$ flight was on Upstate Airlines)?

Decide whether the two events listed are independent. -A fair die is rolled twice. F is the event that six appears on the first roll and $S$ is the event that six appears on the second roll.

Find the odds in favor of the indicated event. -Rolling a 4 with a fair die.

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set. - $\mathrm{L} \cap \mathrm{K}$

Algebra and Equations

Graphs, Lines, and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Mathematics of Finance

Systems of Linear Equations and Matrices

Linear Programming

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Integral Calculus

Multivariate Calculus

Filters

Exam 8: Sets and Probability

Tell whether the statement is true or false. - {4,8,13}={0,4,8,13}\{4,8,13\}=\{0,4,8,13\}{4,8,13}={0,4,8,13}

Find the probability. -A calculator requires a keystroke assembly and a logic circuit. Assume that 80%80 \%80% of the keystroke assemblies and 81%81 \%81% of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory.

Use the given table to find the indicated probability. -People were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. P(\mathrm{P}(P( person is over 40 | person drinks root beer)?

Use a Venn diagram to decide if the statement is true or false. - (A′∩B)′=A∩B′\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)^{\prime}=\mathrm{A} \cap \mathrm{B}^{\prime}(A′∩B)′=A∩B′

Decide whether the statement is true or false. - {15,14,7}∩∅={15,14,7}\{15,14,7\} \cap \varnothing=\{15,14,7\}{15,14,7}∩∅={15,14,7}

Write the word or phrase that best completes each statement or answers thequestion. -If P(A)=P(A∣B)P(A)=P(A \mid B)P(A)=P(A∣B) , why must P(B)=P(B∣A)P(B)=P(B \mid A)P(B)=P(B∣A) ?

A die is rolled twice. Write the indicated event in set notation. -The first roll is a 2 and so is the second.

Find the odds in favor of the indicated event. -Randomly drawing a 4 from the cards pictured below.

Use the given table to find the indicated probability. -The following table contains data from a study of two airlines which fly to Smalltown, USA. P(flight arrived on time nnn flight was on Upstate Airlines)?

Decide whether the two events listed are independent. -A fair die is rolled twice. F is the event that six appears on the first roll and SSS is the event that six appears on the second roll.

Find the odds in favor of the indicated event. -Rolling a 4 with a fair die.

Let U\mathrm{U}U be the smallest possible universal set that includes all of the crops listed; and let A,K\mathrm{A}, \mathrm{K}A,K , and L\mathrm{L}L be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set. - L∩K\mathrm{L} \cap \mathrm{K}L∩K

Algebra and Equations

Graphs, Lines, and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Mathematics of Finance

Systems of Linear Equations and Matrices

Linear Programming

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Integral Calculus

Multivariate Calculus

Filters

Tell whether the statement is true or false. - $\{4,8,13\}=\{0,4,8,13\}$

Find the probability. -A calculator requires a keystroke assembly and a logic circuit. Assume that $80 \%$ of the keystroke assemblies and $81 \%$ of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory.

Decide whether the statement is true or false. - $\{15,14,7\} \cap \varnothing=\{15,14,7\}$

Write the word or phrase that best completes each statement or answers thequestion. -If $P(A)=P(A \mid B)$ , why must $P(B)=P(B \mid A)$ ?

Use the given table to find the indicated probability. -The following table contains data from a study of two airlines which fly to Smalltown, USA. P(flight arrived on time $n$ flight was on Upstate Airlines)?

Decide whether the two events listed are independent. -A fair die is rolled twice. F is the event that six appears on the first roll and $S$ is the event that six appears on the second roll.

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set. - $\mathrm{L} \cap \mathrm{K}$