Question 1

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

Accepted Answer

A)    
B)    
A)    
B)    B

Question 2

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.
-$(A \cup B)^{\prime}$

Accepted Answer

A)  $\{\mathrm{s}, \mathrm{u}, \mathrm{w}\}$ 
B)  $\{t, v, x\}$ 
C)  $\{\mathrm{r}, \mathrm{s}, \mathrm{t}, \mathrm{u}, \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{z}\}$ 
D)  $\{r, t, v, x\}$ 
A)  $\{\mathrm{s}, \mathrm{u}, \mathrm{w}\}$ 
B)  $\{t, v, x\}$ 
C)  $\{\mathrm{r}, \mathrm{s}, \mathrm{t}, \mathrm{u}, \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{z}\}$ 
D)  $\{r, t, v, x\}$ D

Question 3

Use a Venn diagram to answer the question.
-A survey of 116 college students was done to find out what elective courses they were taking. Let $\mathrm{A}=$ the set of those taking art; $\mathrm{B}=$ the set of those taking basket weaving; and $\mathrm{C}=$ the set of those taking canoeing. The study revealed the following information:
$\mathrm{n}(\mathrm{A})=45 ; \mathrm{n}(\mathrm{B})=55 ; \mathrm{n}(\mathrm{C})=40$;
$\mathrm{n}(\mathrm{A} \cap \mathrm{B})=12 ; \mathrm{n}(\mathrm{A} \cap \mathrm{C})=15 ; \mathrm{n}(\mathrm{B} \cap \mathrm{C})=23$;
$\mathrm{n}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=2$.
How many students were not taking any of these electives?

Accepted Answer

A)  24 
B)  34 
C)  10 
D)  26 
A)  24 
B)  34 
C)  10 
D)  26 A

Question 4

Solve the problem.
-One card is selected from a deck of cards. Find the probability of selecting a black card or a card less than 4. (Note: The ace is considered a low card.)

Accepted Answer

A)  $\frac{17}{26}$ 
B)  $\frac{15}{26}$ 
C)  $\frac{8}{13}$ 
D)  $\frac{35}{52}$ 
A)  $\frac{17}{26}$ 
B)  $\frac{15}{26}$ 
C)  $\frac{8}{13}$ 
D)  $\frac{35}{52}$

Question 5

Decide whether the statement is true or false.
-$\{8,5,9\} \cup\{8,5,9\}=\varnothing$

Accepted Answer

A) True 
 B)False

Question 6

Can an event $E$ for a sample space $S$ contain an outcome that is not in $S$ ?

Accepted Answer

A) True 
 B)False

Question 7

Find the probability of the given event.
-A card drawn from a well-shuffled deck of 52 cards is an ace or a 7.

Accepted Answer

A)  $\frac{2}{13}$ 
B)  8 
C)  $\frac{13}{2}$ 
D)  $\frac{4}{13}$ 
A)  $\frac{2}{13}$ 
B)  8 
C)  $\frac{13}{2}$ 
D)  $\frac{4}{13}$

Question 8

Find the number of subsets of the set.
-$\{0\}$

Accepted Answer

A)  1 
B)  4 
C)  0 
D)  2 
A)  1 
B)  4 
C)  0 
D)  2

Question 9

Find the number of subsets of the set.
-$\{1,2,3, \ldots, 9\}$

Accepted Answer

A)  508 
B)  16 
C)  1024 
D)  512 
A)  508 
B)  16 
C)  1024 
D)  512

Question 10

If $A$ and $B$ are outcomes for the same sample space $S$, must $A^{\prime} \cup B^{\prime}$ be an event of $S$ ?

Accepted Answer

A) True 
 B)False

Question 11

Solve the problem.
-If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is a spade, given that the first card was a spade.

Accepted Answer

A)  $\frac{11}{51}$ 
B)  $\frac{4}{17}$ 
C)  $\frac{11}{12}$ 
D)  $\frac{3}{13}$ 
A)  $\frac{11}{51}$ 
B)  $\frac{4}{17}$ 
C)  $\frac{11}{12}$ 
D)  $\frac{3}{13}$

Question 12

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.
  
-$\$ 50,000$ and over

Accepted Answer

A)  .24 
B)  .22 
C)  .25 
D)  .28 
A)  .24 
B)  .22 
C)  .25 
D)  .28

Question 13

Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary.
-For two events $M$ and $N, P(M)=.4, P(N \mid M)=.6$, and $P\left(N \mid M^{\prime}\right)=.2$. Find $P\left(M^{\prime} \mid N\right)$.

Accepted Answer

A)  .33 
B)  .67 
C)  0 
D)  1.0 
A)  .33 
B)  .67 
C)  0 
D)  1.0

Question 14

A die is rolled twice. Write the indicated event in set notation.
-Both rolls are even.

Accepted Answer

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

Question 15

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.
-Exactly 2 belong to an ethnic minority.

Accepted Answer

A) .1990 
B)  .0028 
C)  1929 
D)  . 2156 
A) .1990 
B)  .0028 
C)  1929 
D)  . 2156

Question 16

Two candidates for a sample space, $S_{1}$ and $S_{2}$, are proposed. $S_{1}=\{H H, H T, T H, T T\}$, and $\mathrm{S}_{2}=\{\mathrm{HH}, \mathrm{TT}$, one $\mathrm{H}$ and one $\mathrm{T}\}$. Is $\mathrm{S}_{1}$ acceptable? Is $\mathrm{S}_{2}$ acceptable?

Accepted Answer

A)  Both $S_{1}$ and $S_{2}$ are acceptable. 
B)  Only $S_{1}$ is acceptable. 
C)  Neither $S_{1}$ nor $S_{2}$ is acceptable. 
D)  Only $S_{2}$ is acceptable. 
A)  Both $S_{1}$ and $S_{2}$ are acceptable. 
B)  Only $S_{1}$ is acceptable. 
C)  Neither $S_{1}$ nor $S_{2}$ is acceptable. 
D)  Only $S_{2}$ is acceptable.

Question 17

Solve the problem.
-The contingency table lists the cross tabulation of whether adults feel their life is exciting, routine, or dull for males and females among the adults chosen.
 
Using the letters in the given table, find the number of respondents in the following set. $\mathrm{R} \cap \mathrm{M}$

Accepted Answer

A)  440 
B)  489 
C)  199 
D)  241 
A)  440 
B)  489 
C)  199 
D)  241

Question 18

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.
-$B \cap(A \cup C)$

Accepted Answer

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

Question 19

Is $\mathrm{P}(\mathrm{A} \mid \mathrm{B})$ always less than or equal to $\mathrm{P}(\mathrm{A})$ ?

Accepted Answer

A) True 
 B)False

Question 20

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result.
-The second marble is blue, given that the first marble is red.

Accepted Answer

A)  $\frac{1}{8}$ 
B)  $\frac{1}{7}$ 
C)  $\frac{1}{4}$ 
D)  $\frac{2}{7}$ 
A)  $\frac{1}{8}$ 
B)  $\frac{1}{7}$ 
C)  $\frac{1}{4}$ 
D)  $\frac{2}{7}$

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

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. - $(A \cup B)^{\prime}$

Solve the problem. -One card is selected from a deck of cards. Find the probability of selecting a black card or a card less than 4. (Note: The ace is considered a low card.)

Decide whether the statement is true or false. - $\{8,5,9\} \cup\{8,5,9\}=\varnothing$

Can an event $E$ for a sample space $S$ contain an outcome that is not in $S$ ?

Find the probability of the given event. -A card drawn from a well-shuffled deck of 52 cards is an ace or a 7.

Find the number of subsets of the set. - $\{0\}$

Find the number of subsets of the set. - $\{1,2,3, \ldots, 9\}$

If $A$ and $B$ are outcomes for the same sample space $S$ , must $A^{\prime} \cup B^{\prime}$ be an event of $S$ ?

Solve the problem. -If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is a spade, given that the first card was a spade.

Solve the problem using Bayes' Theorem. Round the answer to the nearest hundredth, if necessary. -For two events $M$ and $N, P(M)=.4, P(N \mid M)=.6$ , and $P\left(N \mid M^{\prime}\right)=.2$ . Find $P\left(M^{\prime} \mid N\right)$ .

A die is rolled twice. Write the indicated event in set notation. -Both rolls are even.

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. -Exactly 2 belong to an ethnic minority.

Two candidates for a sample space, $S_{1}$ and $S_{2}$ , are proposed. $S_{1}=\{H H, H T, T H, T T\}$ , and $\mathrm{S}_{2}=\{\mathrm{HH}, \mathrm{TT}$ , one $\mathrm{H}$ and one $\mathrm{T}\}$ . Is $\mathrm{S}_{1}$ acceptable? Is $\mathrm{S}_{2}$ acceptable?

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. - $B \cap(A \cup C)$

Is $\mathrm{P}(\mathrm{A} \mid \mathrm{B})$ always less than or equal to $\mathrm{P}(\mathrm{A})$ ?

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result. -The second marble is blue, given that the first marble is red.

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

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

Solve the problem. -One card is selected from a deck of cards. Find the probability of selecting a black card or a card less than 4. (Note: The ace is considered a low card.)

Decide whether the statement is true or false. - {8,5,9}∪{8,5,9}=∅\{8,5,9\} \cup\{8,5,9\}=\varnothing{8,5,9}∪{8,5,9}=∅

Can an event EEE for a sample space SSS contain an outcome that is not in SSS ?

Find the probability of the given event. -A card drawn from a well-shuffled deck of 52 cards is an ace or a 7.

Find the number of subsets of the set. - {0}\{0\}{0}

Find the number of subsets of the set. - {1,2,3,…,9}\{1,2,3, \ldots, 9\}{1,2,3,…,9}

If AAA and BBB are outcomes for the same sample space SSS , must A′∪B′A^{\prime} \cup B^{\prime}A′∪B′ be an event of SSS ?

Solve the problem. -If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is a spade, given that the first card was a spade.

A die is rolled twice. Write the indicated event in set notation. -Both rolls are even.

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. -Exactly 2 belong to an ethnic minority.

Is P(A∣B)\mathrm{P}(\mathrm{A} \mid \mathrm{B})P(A∣B) always less than or equal to P(A)\mathrm{P}(\mathrm{A})P(A) ?

Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability of the indicated result. -The second marble is blue, given that the first marble is red.

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

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

Decide whether the statement is true or false. - $\{8,5,9\} \cup\{8,5,9\}=\varnothing$

Can an event $E$ for a sample space $S$ contain an outcome that is not in $S$ ?

Find the number of subsets of the set. - $\{0\}$

Find the number of subsets of the set. - $\{1,2,3, \ldots, 9\}$

If $A$ and $B$ are outcomes for the same sample space $S$ , must $A^{\prime} \cup B^{\prime}$ be an event of $S$ ?

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. -Exactly 2 belong to an ethnic minority.

Is $\mathrm{P}(\mathrm{A} \mid \mathrm{B})$ always less than or equal to $\mathrm{P}(\mathrm{A})$ ?