Question 1

Tell whether the statement is true or false.
-$\{2,12,26,7,32\}=\{32,12,7,62,2\}$

Accepted Answer

A) True 
 B)False

Question 2

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.
-$\mathrm{n}(\mathrm{A})=85, \mathrm{n}(\mathrm{B})=93, \mathrm{n}(\mathrm{C})=87, \mathrm{n}(\mathrm{A} \cap \mathrm{B})=17, \mathrm{n}(\mathrm{A} \cap \mathrm{C})=19, \mathrm{n}(\mathrm{B} \cap \mathrm{C})=13, \mathrm{n}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=11$, and $\mathrm{n}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime} \cap \mathrm{C}^{\prime}\right)=171$. Find $\mathrm{n}(\mathrm{U})$

Accepted Answer

A)  227 
B)  398 
C)  408 
D)  312 
A)  227 
B)  398 
C)  408 
D)  312

Question 3

Suppose P(C) = .048, P(M ꓵ C) = .044, and P(M ꓴ C) = .524. Find the indicated probability.
-P( M)

Accepted Answer

A)   520 
B)   472 
C)  480 
D)   528 
A)   520 
B)   472 
C)  480 
D)   528

Question 4

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.
-$n(U)=118, n(A)=37, n(B)=50, n(C)=43, n(A \cap B)=8, n(A \cap C)=6, n(B \cap C)=7$, and $n(A \cap(B \cap C))=5$. Find $n\left(((A \cup B) \cup C)^{\prime}\right)$.

Accepted Answer

A)  5 
B)  32 
C)  4 
D)  28 
A)  5 
B)  32 
C)  4 
D)  28

Question 5

Suppose P(C) = .048, P(M ꓵ C) = .044, and P(M ꓴ C) = .524. Find the indicated probability.
-$\mathrm{P}\left(\mathrm{M}^{\prime} \cap \mathrm{C}^{\prime}\right)$

Accepted Answer

A)   568 
B)   476 
C)   956 
D)   564 
A)   568 
B)   476 
C)   956 
D)   564

Question 6

A die is rolled twice. Write the indicated event in set notation.
-The sum of the rolls is 7 , and one roll is a 1.

Accepted Answer

A)  $\{(1,6),(6,1)\}$ 
B)  $\{(1,6)\}$ 
C)  $\varnothing$ 
D)  $\{(6,1)\}$ 
A)  $\{(1,6),(6,1)\}$ 
B)  $\{(1,6)\}$ 
C)  $\varnothing$ 
D)  $\{(6,1)\}$

Question 7

For the experiment described, write the indicated event in set notation.
-A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space: The second toss shows a one.

Accepted Answer

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

Question 8

Insert " $\subseteq$ " or "q" in the blank to make the statement true.
-{k, b, d} _{k, b, d}

Accepted Answer

A)  $\nsubseteq$ 
B)  $\subseteq$ 
A)  $\nsubseteq$ 
B)  $\subseteq$

Question 9

Tell whether the statement is true or false.
-$\{57,58,57,58\}=\{57,58\}$

Accepted Answer

A) True 
 B)False

Question 10

Write the sample space for the given experiment.
-A box contains 2 blue cards numbered 1 through 2 , and 3 green cards numbered 1 through 3 . A blue card is picked, followed by a green card.

Accepted Answer

A)  $\{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3)\}$ 
B)  $\{12\}$ 
C)  $\{(1,1),(1,2),(2,1),(2,2),(3,1),(3,2)\}$ 
D)  $\{7\}$ 
A)  $\{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3)\}$ 
B)  $\{12\}$ 
C)  $\{(1,1),(1,2),(2,1),(2,2),(3,1),(3,2)\}$ 
D)  $\{7\}$

Question 11

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.
  
-$\$ 20,000$ - $\$ 24,999$

Accepted Answer

A)  .07 
B)  .11 
C)  .06 
D)  .08 
A)  .07 
B)  .11 
C)  .06 
D)  .08

Question 12

If $A$ and $B$ are independent events, how many of the following statements must be true?
(i) A' and B are independent.
(ii) $\mathrm{A}$ and $\mathrm{B}^{\prime}$ are independent.
(iii) $\mathrm{A}^{\prime}$ and $\mathrm{B}^{\prime}$ are independent.

Accepted Answer

A) A 11 
B)  One 
C)  None 
D)  Two 
A) A 11 
B)  One 
C)  None 
D)  Two

Question 13

Assume that, at a certain college, $33 \%$ of all physics majors belong to ethnic minorities. Given a random sample of 10physics majors, find the probability of the indicated event. Round your answer as appropriate.
-Only the last 4 do not belong to an ethnic minority.

Accepted Answer

A)  .01186 
B) .09046 
C)  20151 
D)  .00026 
A)  .01186 
B) .09046 
C)  20151 
D)  .00026

Question 14

Insert " $\subseteq$ " or "q" in the blank to make the statement true.
-$\{b, c, h, f\}-\{b, c, h, f, k\}$

Accepted Answer

A)  $\subseteq$ 
B)  $\nsubseteq$ 
A)  $\subseteq$ 
B)  $\nsubseteq$

Question 15

Shade the Venn diagram to represent the set.
-$(A \cap B) \cup(A \cup B)^{\prime}$

Accepted Answer

A)    
B)    
A)    
B)

Question 16

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.
  
-$\$ 30,000-\$ 39,999$

Accepted Answer

A) . 14 
B)  .03 
C)  .26 
D)  .13 
A) . 14 
B)  .03 
C)  .26 
D)  .13

Question 17

Decide whether the statement is true or false.
-$\varnothing \cap \varnothing=\varnothing$

Accepted Answer

A) True 
 B)False

Question 18

Solve the problem. Express the answer as a percentage.
-A coin is biased to show $37 \%$ heads and $63 \%$ tails. The coin is tossed twice. What is the probability that the coin turns up heads once and tails once?

Accepted Answer

A)  $46.62 \%$ 
B)  $37 \%$ 
C)  $23.31 \%$ 
D)  $63 \%$ 
A)  $46.62 \%$ 
B)  $37 \%$ 
C)  $23.31 \%$ 
D)  $63 \%$

Question 19

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.
-L' $\cap$ A

Accepted Answer

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

Question 20

Solve the problem.
-A survey of senior citizens at a doctor's office shows that $56 \%$ take blood pressure-lowering medication, $41 \%$ take cholesterol-lowering medication, and $3 \%$ take both medications. What is the probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering medication? Express the answer as a percentage

Accepted Answer

A)  $0 \%$ 
B)  $100 \%$ 
C)  $18 \%$ 
D)  $94 \%$ 
A)  $0 \%$ 
B)  $100 \%$ 
C)  $18 \%$ 
D)  $94 \%$

Tell whether the statement is true or false. - $\{2,12,26,7,32\}=\{32,12,7,62,2\}$

Suppose P(C) = .048, P(M ꓵ C) = .044, and P(M ꓴ C) = .524. Find the indicated probability. -P( M)

Use a Venn Diagram and the given information to determine the number of elements in the indicated set. - $n(U)=118, n(A)=37, n(B)=50, n(C)=43, n(A \cap B)=8, n(A \cap C)=6, n(B \cap C)=7$ , and $n(A \cap(B \cap C))=5$ . Find $n\left(((A \cup B) \cup C)^{\prime}\right)$ .

Suppose P(C) = .048, P(M ꓵ C) = .044, and P(M ꓴ C) = .524. Find the indicated probability. - $\mathrm{P}\left(\mathrm{M}^{\prime} \cap \mathrm{C}^{\prime}\right)$

A die is rolled twice. Write the indicated event in set notation. -The sum of the rolls is 7 , and one roll is a 1.

For the experiment described, write the indicated event in set notation. -A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space: The second toss shows a one.

Insert " $\subseteq$ " or "q" in the blank to make the statement true. -{k, b, d} _{k, b, d}

Tell whether the statement is true or false. - $\{57,58,57,58\}=\{57,58\}$

Write the sample space for the given experiment. -A box contains 2 blue cards numbered 1 through 2 , and 3 green cards numbered 1 through 3 . A blue card is picked, followed by a green card.

If $A$ and $B$ are independent events, how many of the following statements must be true? (i) A' and B are independent. (ii) $\mathrm{A}$ and $\mathrm{B}^{\prime}$ are independent. (iii) $\mathrm{A}^{\prime}$ and $\mathrm{B}^{\prime}$ are independent.

Assume that, at a certain college, $33 \%$ of all physics majors belong to ethnic minorities. Given a random sample of 10physics majors, find the probability of the indicated event. Round your answer as appropriate. -Only the last 4 do not belong to an ethnic minority.

Insert " $\subseteq$ " or "q" in the blank to make the statement true. - $\{b, c, h, f\}-\{b, c, h, f, k\}$

Shade the Venn diagram to represent the set. - $(A \cap B) \cup(A \cup B)^{\prime}$ $Shade the Venn diagram to represent the set. - (A \cap B) \cup(A \cup B)^{\prime}$

Decide whether the statement is true or false. - $\varnothing \cap \varnothing=\varnothing$

Solve the problem. Express the answer as a percentage. -A coin is biased to show $37 \%$ heads and $63 \%$ tails. The coin is tossed twice. What is the probability that the coin turns up heads once and tails once?

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. -L' $\cap$ A

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. - {2,12,26,7,32}={32,12,7,62,2}\{2,12,26,7,32\}=\{32,12,7,62,2\}{2,12,26,7,32}={32,12,7,62,2}

Suppose P(C) = .048, P(M ꓵ C) = .044, and P(M ꓴ C) = .524. Find the indicated probability. -P( M)

Suppose P(C) = .048, P(M ꓵ C) = .044, and P(M ꓴ C) = .524. Find the indicated probability. - P(M′∩C′)\mathrm{P}\left(\mathrm{M}^{\prime} \cap \mathrm{C}^{\prime}\right)P(M′∩C′)

A die is rolled twice. Write the indicated event in set notation. -The sum of the rolls is 7 , and one roll is a 1.

For the experiment described, write the indicated event in set notation. -A die is tossed twice with the tosses recorded as an ordered pair. Represent the following event as a subset of the sample space: The second toss shows a one.

Insert " ⊆\subseteq⊆ " or "q" in the blank to make the statement true. -{k, b, d} _{k, b, d}

Tell whether the statement is true or false. - {57,58,57,58}={57,58}\{57,58,57,58\}=\{57,58\}{57,58,57,58}={57,58}

Write the sample space for the given experiment. -A box contains 2 blue cards numbered 1 through 2 , and 3 green cards numbered 1 through 3 . A blue card is picked, followed by a green card.

If AAA and BBB are independent events, how many of the following statements must be true? (i) A' and B are independent. (ii) A\mathrm{A}A and B′\mathrm{B}^{\prime}B′ are independent. (iii) A′\mathrm{A}^{\prime}A′ and B′\mathrm{B}^{\prime}B′ are independent.

Assume that, at a certain college, 33%33 \%33% of all physics majors belong to ethnic minorities. Given a random sample of 10physics majors, find the probability of the indicated event. Round your answer as appropriate. -Only the last 4 do not belong to an ethnic minority.

Insert " ⊆\subseteq⊆ " or "q" in the blank to make the statement true. - {b,c,h,f}−{b,c,h,f,k}\{b, c, h, f\}-\{b, c, h, f, k\}{b,c,h,f}−{b,c,h,f,k}

Shade the Venn diagram to represent the set. - (A∩B)∪(A∪B)′(A \cap B) \cup(A \cup B)^{\prime}(A∩B)∪(A∪B)′

Decide whether the statement is true or false. - ∅∩∅=∅\varnothing \cap \varnothing=\varnothing∅∩∅=∅

Solve the problem. Express the answer as a percentage. -A coin is biased to show 37%37 \%37% heads and 63%63 \%63% tails. The coin is tossed twice. What is the probability that the coin turns up heads once and tails once?

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' ∩\cap∩ A

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. - $\{2,12,26,7,32\}=\{32,12,7,62,2\}$

Suppose P(C) = .048, P(M ꓵ C) = .044, and P(M ꓴ C) = .524. Find the indicated probability. - $\mathrm{P}\left(\mathrm{M}^{\prime} \cap \mathrm{C}^{\prime}\right)$

Insert " $\subseteq$ " or "q" in the blank to make the statement true. -{k, b, d} _{k, b, d}

Tell whether the statement is true or false. - $\{57,58,57,58\}=\{57,58\}$

If $A$ and $B$ are independent events, how many of the following statements must be true? (i) A' and B are independent. (ii) $\mathrm{A}$ and $\mathrm{B}^{\prime}$ are independent. (iii) $\mathrm{A}^{\prime}$ and $\mathrm{B}^{\prime}$ are independent.

Assume that, at a certain college, $33 \%$ of all physics majors belong to ethnic minorities. Given a random sample of 10physics majors, find the probability of the indicated event. Round your answer as appropriate. -Only the last 4 do not belong to an ethnic minority.

Insert " $\subseteq$ " or "q" in the blank to make the statement true. - $\{b, c, h, f\}-\{b, c, h, f, k\}$

Shade the Venn diagram to represent the set. - $(A \cap B) \cup(A \cup B)^{\prime}$ $Shade the Venn diagram to represent the set. - (A \cap B) \cup(A \cup B)^{\prime}$

Decide whether the statement is true or false. - $\varnothing \cap \varnothing=\varnothing$

Solve the problem. Express the answer as a percentage. -A coin is biased to show $37 \%$ heads and $63 \%$ tails. The coin is tossed twice. What is the probability that the coin turns up heads once and tails once?

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. -L' $\cap$ A