Question 1

Write the sample space for the given experiment.
-A group of 12 people are assigned numbers 1 through 12. A person assigned a number of 5 or less is chosen.

Accepted Answer

A)  $\{1\}$ 
B)  $\{1,2,3,4,5\}$ 
C)  $\{12\}$ 
D)  $\{1,2,3,4\}$ 
A)  $\{1\}$ 
B)  $\{1,2,3,4,5\}$ 
C)  $\{12\}$ 
D)  $\{1,2,3,4\}$

Question 2

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.
  
-$\$ 25,000-\$ 29,999$

Accepted Answer

A)  .14 
B)  .13 
C)  .07 
D)  .09 
A)  .14 
B)  .13 
C)  .07 
D)  .09

Question 3

Find the number of subsets of the set.
-$\{x \mid x$ is an even number between 15 and 35$\}$

Accepted Answer

A)  1024 
B)  32 
C)  34 
D)  5 
A)  1024 
B)  32 
C)  34 
D)  5

Question 4

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

Accepted Answer

A)  0 
B)   956 
C)   476 
D)   952 
A)  0 
B)   956 
C)   476 
D)   952

Question 5

Find the probability.
-A basketball player hits her shot $42 \%$ of the time. If she takes four shots during a game, what is the probability that she misses the first shot and hits the last three? Express the answer as a percentage, and round to the nearest tenth (if necessary).

Accepted Answer

A)  $4.3 \%$ 
B)  $3.1 \%$ 
C)  $31.1 \%$ 
D)  $43 \%$ 
A)  $4.3 \%$ 
B)  $3.1 \%$ 
C)  $31.1 \%$ 
D)  $43 \%$

Question 6

Solve the problem. Express the answer as a percentage.
-A coin is biased to show $41 \%$ heads and $59 \%$ tails. The coin is tossed twice. What is the probability that the coin turns up tails on both tosses?

Accepted Answer

A)  $34.81 \%$ 
B)  $18 \%$ 
C)  $59 \%$ 
D)  $41 \%$ 
A)  $34.81 \%$ 
B)  $18 \%$ 
C)  $59 \%$ 
D)  $41 \%$

Question 7

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.
-$n(U)=87, n(A)=23, n(B)=30, n(C)=53, n(A \cap B)=6, n(A \cap C)=9, n(B \cap C)=8$, and $\mathrm{n}(\mathrm{A} \cap(\mathrm{B} \cap \mathrm{C}))=4$. Find $\mathrm{n}(\mathrm{A} \cap(\mathrm{B} \cap \mathrm{C}))$.

Accepted Answer

A)  3 
B)  4 
C)  12 
D)  15 
A)  3 
B)  4 
C)  12 
D)  15

Question 8

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.
-On ly the first 2 belong to an ethnic minority.

Accepted Answer

A) . 1111 
B)  .1990 
C)  .1089 
D) . 0044 
A) . 1111 
B)  .1990 
C)  .1089 
D) . 0044

Question 9

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

Accepted Answer

A)    
B)    
A)    
B)

Question 10

Use the given table to find the indicated probability.
-College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results.
 
$\mathrm{P}($ favorite topping is veggie $\mid$ student is junior or senior)?
Round the answer to the nearest hundredth.

Accepted Answer

A)  .592 
B)  .202 
C)  .389 
D)  .407 
A)  .592 
B)  .202 
C)  .389 
D)  .407

Question 11

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.
-No more than 6 belong to an ethnic minority.

Accepted Answer

A)  .9815 
B)  .9846 
C)  .913 
D)  .0547 
A)  .9815 
B)  .9846 
C)  .913 
D)  .0547

Question 12

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 drinks root beer $\mid$ person is over 40$)$ ?

Accepted Answer

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

Question 13

A sample space $S$ is a set of 6 outcomes. What is the least number of outcomes that an event defined for $S$ can have?

Accepted Answer

A)  6 
B)  1 
C)  720 
D)  0 
A)  6 
B)  1 
C)  720 
D)  0

Question 14

Use a Venn diagram to decide if the statement is true or false.
-$(A \cap B) \cup C=(A \cup C) \cap(A \cup B)$

Accepted Answer

A) True 
 B)False

Question 15

Solve the problem.
-One card is selected from a deck of cards. Find the probability of selecting a diamond or a card less than 6. (Note: The ace is considered a low card.)

Accepted Answer

A)  $\frac{25}{52}$ 
B)  $\frac{8}{13}$ 
C)  $\frac{7}{13}$ 
D)  $\frac{27}{52}$ 
A)  $\frac{25}{52}$ 
B)  $\frac{8}{13}$ 
C)  $\frac{7}{13}$ 
D)  $\frac{27}{52}$

Question 16

Find the probability of the given event.
-A bag contains 4 red marbles, 6 blue marbles, and 9 green marbles. A randomly drawn marble is blue.

Accepted Answer

A)  $\frac{3}{5}$ 
B)  $\frac{4}{19}$ 
C)  $\frac{6}{19}$ 
D)  $\frac{9}{19}$ 
A)  $\frac{3}{5}$ 
B)  $\frac{4}{19}$ 
C)  $\frac{6}{19}$ 
D)  $\frac{9}{19}$

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

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 first toss shows a one.

Accepted Answer

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

Question 19

Decide whether the two events listed are independent.
-A fair die is rolled twice. $E$ is the event that the sum of the two rolls is eight and $T$ is the event that three appears on the first roll.

Accepted Answer

A) True 
 B)False

Question 20

Solve the problem.
-Among 170 households surveyed, 58 have a video camera, 56 have a snapshot camera, 21 have binoculars, 4 have a video camera and a snapshot camera, 8 have a snapshot camera and binoculars, and 2 have all three products. What is the probability that a household will have a snapshot camera or binoculars? Express the answer as a fraction.

Accepted Answer

A)  $\frac{57}{85}$ 
B)  $\frac{69}{170}$ 
C)  $\frac{77}{170}$ 
D)  $\frac{53}{85}$ 
A)  $\frac{57}{85}$ 
B)  $\frac{69}{170}$ 
C)  $\frac{77}{170}$ 
D)  $\frac{53}{85}$

Write the sample space for the given experiment. -A group of 12 people are assigned numbers 1 through 12. A person assigned a number of 5 or less is chosen.

Find the number of subsets of the set. - $\{x \mid x$ is an even number between 15 and 35 $\}$

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

Find the probability. -A basketball player hits her shot $42 \%$ of the time. If she takes four shots during a game, what is the probability that she misses the first shot and hits the last three? Express the answer as a percentage, and round to the nearest tenth (if necessary).

Solve the problem. Express the answer as a percentage. -A coin is biased to show $41 \%$ heads and $59 \%$ tails. The coin is tossed twice. What is the probability that the coin turns up tails on both tosses?

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. -On ly the first 2 belong to an ethnic minority.

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

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. -No more than 6 belong to an ethnic minority.

A sample space $S$ is a set of 6 outcomes. What is the least number of outcomes that an event defined for $S$ can have?

Use a Venn diagram to decide if the statement is true or false. - $(A \cap B) \cup C=(A \cup C) \cap(A \cup B)$ $Use a Venn diagram to decide if the statement is true or false. - (A \cap B) \cup C=(A \cup C) \cap(A \cup B)$

Solve the problem. -One card is selected from a deck of cards. Find the probability of selecting a diamond or a card less than 6. (Note: The ace is considered a low card.)

Find the probability of the given event. -A bag contains 4 red marbles, 6 blue marbles, and 9 green marbles. A randomly drawn marble is blue.

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 first toss shows a one.

Decide whether the two events listed are independent. -A fair die is rolled twice. $E$ is the event that the sum of the two rolls is eight and $T$ is the event that three appears on the first roll.

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

Write the sample space for the given experiment. -A group of 12 people are assigned numbers 1 through 12. A person assigned a number of 5 or less is chosen.

Find the number of subsets of the set. - {x∣x\{x \mid x{x∣x is an even number between 15 and 35 }\}}

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} \cup \mathrm{C})^{\prime}\right]P[(M∪C)′]

Find the probability. -A basketball player hits her shot 42%42 \%42% of the time. If she takes four shots during a game, what is the probability that she misses the first shot and hits the last three? Express the answer as a percentage, and round to the nearest tenth (if necessary).

Solve the problem. Express the answer as a percentage. -A coin is biased to show 41%41 \%41% heads and 59%59 \%59% tails. The coin is tossed twice. What is the probability that the coin turns up tails on both tosses?

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. -On ly the first 2 belong to an ethnic minority.

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

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. -No more than 6 belong to an ethnic minority.

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 drinks root beer ∣\mid∣ person is over 40 ))) ?

A sample space SSS is a set of 6 outcomes. What is the least number of outcomes that an event defined for SSS can have?

Use a Venn diagram to decide if the statement is true or false. - (A∩B)∪C=(A∪C)∩(A∪B)(A \cap B) \cup C=(A \cup C) \cap(A \cup B)(A∩B)∪C=(A∪C)∩(A∪B)

Solve the problem. -One card is selected from a deck of cards. Find the probability of selecting a diamond or a card less than 6. (Note: The ace is considered a low card.)

Find the probability of the given event. -A bag contains 4 red marbles, 6 blue marbles, and 9 green marbles. A randomly drawn marble is blue.

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

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 first toss shows a one.

Decide whether the two events listed are independent. -A fair die is rolled twice. EEE is the event that the sum of the two rolls is eight and TTT is the event that three appears on the first roll.

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

Find the number of subsets of the set. - $\{x \mid x$ is an even number between 15 and 35 $\}$

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

Find the probability. -A basketball player hits her shot $42 \%$ of the time. If she takes four shots during a game, what is the probability that she misses the first shot and hits the last three? Express the answer as a percentage, and round to the nearest tenth (if necessary).

Solve the problem. Express the answer as a percentage. -A coin is biased to show $41 \%$ heads and $59 \%$ tails. The coin is tossed twice. What is the probability that the coin turns up tails on both tosses?

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. -On ly the first 2 belong to an ethnic minority.

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

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. -No more than 6 belong to an ethnic minority.

A sample space $S$ is a set of 6 outcomes. What is the least number of outcomes that an event defined for $S$ can have?

Use a Venn diagram to decide if the statement is true or false. - $(A \cap B) \cup C=(A \cup C) \cap(A \cup B)$ $Use a Venn diagram to decide if the statement is true or false. - (A \cap B) \cup C=(A \cup C) \cap(A \cup B)$

Decide whether the two events listed are independent. -A fair die is rolled twice. $E$ is the event that the sum of the two rolls is eight and $T$ is the event that three appears on the first roll.