Question 1

A die is rolled twice. Write the indicated event in set notation.
-The sum of the rolls is either 7 or 9 , and one roll is a 4 .

Accepted Answer

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

Question 2

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 was on Upstate Airlines | flight arrived late)?

Accepted Answer

A)  $\frac{5}{87}$ 
B)  $\frac{5}{11}$ 
C)  $\frac{5}{48}$ 
D)  None of the above 
A)  $\frac{5}{87}$ 
B)  $\frac{5}{11}$ 
C)  $\frac{5}{48}$ 
D)  None of the above

Question 3

Solve the problem.
-One card is selected from a deck of cards. Find the probability of selecting a red card or a heart.

Accepted Answer

A)  $\frac{1}{2}$ 
B)  $\frac{3}{4}$ 
C)  $\frac{1}{4}$ 
D)  0 
A)  $\frac{1}{2}$ 
B)  $\frac{3}{4}$ 
C)  $\frac{1}{4}$ 
D)  0

Question 4

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.
-$\mathrm{A}^{\prime} \cup \mathrm{L}$

Accepted Answer

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

Question 5

An experiment is conducted for which the sample space is $S$ assignment ispossible for this experiment.
-

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

A)   004 
B)   956 
C)   524 
D)   466 
A)   004 
B)   956 
C)   524 
D)   466

Question 7

Convert the odds that the given event will occur to the probability that the event will occur.
-The odds in favor of winning a particular lottery are 1 to $2,300,000$.

Accepted Answer

A)  $\frac{1}{2,300,001}$ 
B)  $\frac{2,300,000}{2,300,001}$ 
C)  $\frac{1}{2,299,999}$ 
D)  $\frac{1}{2,300,000}$ 
A)  $\frac{1}{2,300,001}$ 
B)  $\frac{2,300,000}{2,300,001}$ 
C)  $\frac{1}{2,299,999}$ 
D)  $\frac{1}{2,300,000}$

Question 8

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 none of the four is pure recessive?

Accepted Answer

A)  .316 
B)  .75 
C) . 0625 
D)  .004 
A)  .316 
B)  .75 
C) . 0625 
D)  .004

Question 9

Provide an appropriate response.
-Given that a student correctly uses the following form of Bayes' theorem,
$\mathrm{P}\left(\mathrm{R}_{1} \mid \mathrm{T}\right)=\frac{\mathrm{P}\left(\mathrm{T} \mid \mathrm{R}_{1}\right) \mathrm{P}\left(\mathrm{R}_{1}\right)}{\mathrm{P}\left(\mathrm{T} \mid \mathrm{R}_{1}\right) \mathrm{P}\left(\mathrm{R}_{1}\right)+\mathrm{P}\left(\mathrm{T} \mid \mathrm{R}_{2}\right) \mathrm{P}\left(\mathrm{R}_{2}\right)+\mathrm{P}\left(\mathrm{T} \mid \mathrm{R}_{3}\right) \mathrm{P}\left(\mathrm{R}_{3}\right)}$,
Make a precise statement about the value of $P\left(R_{1} \cup R_{2} \cup R_{3}\right)$.

Accepted Answer

A)  $0<$ P $<1$ 
B)  $\mathrm{P}=0$ 
C)  $0 \leq \mathrm{P} \leq 1$ 
D)  $\mathrm{P}=1$ 
A)  $0<$ P $<1$ 
B)  $\mathrm{P}=0$ 
C)  $0 \leq \mathrm{P} \leq 1$ 
D)  $\mathrm{P}=1$

Question 10

A die is rolled twice. Write the indicated event in set notation.
-The sum of the rolls is 13.

Accepted Answer

A)  $\{(7,6)\}$ 
B)  $\{(6,7)\}$ 
C)  $\varnothing$ 
D)  $\{(6,7),(7,6)\}$ 
A)  $\{(7,6)\}$ 
B)  $\{(6,7)\}$ 
C)  $\varnothing$ 
D)  $\{(6,7),(7,6)\}$

Question 11

Determine whether the given events are disjoint.
-Drawing a face card from a deck of cards and drawing a deuce

Accepted Answer

A) True 
 B)False

Question 12

Use the given table to find the probability of the indicated event. Round your answer to the nearest thousandth.
-College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results.
 
A randomly selected student prefers a cheese topping.

Accepted Answer

A)   348 
B)   050 
C)   490 
D)   143 
A)   348 
B)   050 
C)   490 
D)   143

Question 13

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.
-One marble is green, and one marble is red.

Accepted Answer

A)  $\frac{1}{7}$ 
B)  $\frac{3}{28}$ 
C)  $\frac{1}{2}$ 
D)  $\frac{1}{4}$ 
A)  $\frac{1}{7}$ 
B)  $\frac{3}{28}$ 
C)  $\frac{1}{2}$ 
D)  $\frac{1}{4}$

Question 14

Find the odds in favor of the indicated event.
-Rolling a number less than 3 with a fair die.

Accepted Answer

A)  2 to 3 
B)  1 to 2 
C)  1 to 1 
D)  1 to 3 
A)  2 to 3 
B)  1 to 2 
C)  1 to 1 
D)  1 to 3

Question 15

An experiment consists of tossing a fair coin 3 times. Is it possible to have an outcome with exactly one head and exactly one tail?

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

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 cola)?

Accepted Answer

A)  $\frac{4}{17}$ 
B)  $\frac{4}{19}$ 
C)  $\frac{4}{51}$ 
D)  None of the above 
A)  $\frac{4}{17}$ 
B)  $\frac{4}{19}$ 
C)  $\frac{4}{51}$ 
D)  None of the above

Question 18

Solve the problem.
-Below is a table of data from a survey given to 1600 teenagers asking them to estimate what percentage of their classmates are using drugs. Find the probability that a randomly selected girl thinks that $50 \%$ or more of her classmates are using drugs. Round your answer to the nearest hundredth.

Accepted Answer

A)  .21 
B)  .18 
C)  .09 
D) . 11 
A)  .21 
B)  .18 
C)  .09 
D) . 11

Question 19

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.
  
-$\$ 10,000$ - $\$ 14,999$

Accepted Answer

A)  .05 
B) .03 
C)  .06 
D)  .02 
A)  .05 
B) .03 
C)  .06 
D)  .02

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.
-Th e second marble is red, given that the first marble is white.

Accepted Answer

A)  $\frac{3}{28}$ 
B)  $\frac{1}{4}$ 
C)  $\frac{2}{7}$ 
D)  $\frac{3}{32}$ 
A)  $\frac{3}{28}$ 
B)  $\frac{1}{4}$ 
C)  $\frac{2}{7}$ 
D)  $\frac{3}{32}$

A die is rolled twice. Write the indicated event in set notation. -The sum of the rolls is either 7 or 9 , and one roll is a 4 .

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 was on Upstate Airlines | flight arrived late)?

Solve the problem. -One card is selected from a deck of cards. Find the probability of selecting a red card or a heart.

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. - $\mathrm{A}^{\prime} \cup \mathrm{L}$

An experiment is conducted for which the sample space is $S$ assignment ispossible for this experiment. -

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

Convert the odds that the given event will occur to the probability that the event will occur. -The odds in favor of winning a particular lottery are 1 to $2,300,000$ .

A die is rolled twice. Write the indicated event in set notation. -The sum of the rolls is 13.

Determine whether the given events are disjoint. -Drawing a face card from a deck of cards and drawing a deuce

Use the given table to find the probability of the indicated event. Round your answer to the nearest thousandth. -College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. A randomly selected student prefers a cheese topping.

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. -One marble is green, and one marble is red.

Find the odds in favor of the indicated event. -Rolling a number less than 3 with a fair die.

An experiment consists of tossing a fair coin 3 times. Is it possible to have an outcome with exactly one head and exactly one tail?

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

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. -Th e second marble is red, given that the first marble is white.

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

A die is rolled twice. Write the indicated event in set notation. -The sum of the rolls is either 7 or 9 , and one roll is a 4 .

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 was on Upstate Airlines | flight arrived late)?

Solve the problem. -One card is selected from a deck of cards. Find the probability of selecting a red card or a heart.

An experiment is conducted for which the sample space is SSS assignment ispossible for this experiment. -

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

Convert the odds that the given event will occur to the probability that the event will occur. -The odds in favor of winning a particular lottery are 1 to 2,300,0002,300,0002,300,000 .

A die is rolled twice. Write the indicated event in set notation. -The sum of the rolls is 13.

Determine whether the given events are disjoint. -Drawing a face card from a deck of cards and drawing a deuce

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. -One marble is green, and one marble is red.

Find the odds in favor of the indicated event. -Rolling a number less than 3 with a fair die.

An experiment consists of tossing a fair coin 3 times. Is it possible to have an outcome with exactly one head and exactly one tail?

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

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 cola)?

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. -Th e second marble is red, given that the first marble is white.

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

An experiment is conducted for which the sample space is $S$ assignment ispossible for this experiment. -

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

Convert the odds that the given event will occur to the probability that the event will occur. -The odds in favor of winning a particular lottery are 1 to $2,300,000$ .