Question 1

Find the indicated probability.
-Two fair dice are rolled. Find the probability that the sum of the two numbers is not greater than 5.

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 5 } { 18 }$ 
D)  $\frac { 13 } { 18 }$ 
A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 5 } { 18 }$ 
D)  $\frac { 13 } { 18 }$

Question 2

Decide whether or not the events are mutually exclusive.
-Events A and B defined as follows Event A is that at least three of Toni's five cousins are female.
Event B is that at least three of Toni's five cousins are male.

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

Question 3

Find the conditional probability.
-If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is red, given that the first card was a heart.

Accepted Answer

A)  $\frac { 26 } { 51 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 25 } { 52 }$ 
D)  $\frac { 25 } { 51 }$ 
A)  $\frac { 26 } { 51 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 25 } { 52 }$ 
D)  $\frac { 25 } { 51 }$

Question 4

Find the indicated probability.
-The following table contains data from a study of two airlines which fly to Small Town, USA.

If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight which was on time.

Accepted Answer

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

Question 5

Two cards are selected without replacement from a standard deck of 52 cards. What is the probability that both cards are the same color (i.e., either both black or both red)?

Accepted Answer

A) 0.490 
B) 0.500 
C) 0.250 
D) 0.245 
A) 0.490 
B) 0.500 
C) 0.250 
D) 0.245

Question 6

Find the probability.
-In one town, 70% of adults have health insurance. What is the probability that 8 adults selected at random from the town all have health insurance?

Accepted Answer

A) 5.6 
B) 0.7 
C) 0.058 
D) 0.114 
A) 5.6 
B) 0.7 
C) 0.058 
D) 0.114

Question 7

Find the conditional probability.
-If three cards are drawn at random without replacement from a standard deck, find the probability that the third card is a face card, given that the first card was a queen and the second card was a 5.

Accepted Answer

A)  $\frac { 6 } { 25 }$ 
B)  $\frac { 3 } { 13 }$ 
C)  $\frac { 11 } { 50 }$ 
D)  $\frac { 1 } { 5 }$ 
A)  $\frac { 6 } { 25 }$ 
B)  $\frac { 3 } { 13 }$ 
C)  $\frac { 11 } { 50 }$ 
D)  $\frac { 1 } { 5 }$

Question 8

Solve the problem.
-The digits 1, 2, 3, 4, 5, and 7 are randomly arranged to form a six-digit number. Find the probability that the first and last digits are both even.

Accepted Answer

A)  $\frac { 1 } { 30 }$ 
B)  $\frac { 1 } { 360 }$ 
C)  $\frac { 1 } { 12 }$ 
D)  $\frac { 1 } { 15 }$ 
A)  $\frac { 1 } { 30 }$ 
B)  $\frac { 1 } { 360 }$ 
C)  $\frac { 1 } { 12 }$ 
D)  $\frac { 1 } { 15 }$

Question 9

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In bridge, 4 aces

Accepted Answer

A) 0.01056 
B) 0.00118 
C) 0.00059 
D) 0.00264 
A) 0.01056 
B) 0.00118 
C) 0.00059 
D) 0.00264

Question 10

Find the indicated probability.
-A card is drawn at random from a standard 52-card deck. Find the probability that the card is neither an ace nor a heart.

Accepted Answer

A)  $\frac { 4 } { 13 }$ 
B)  $\frac { 9 } { 13 }$ 
C)  $\frac { 21 } { 26 }$ 
D)  $\frac { 35 } { 52 }$ 
A)  $\frac { 4 } { 13 }$ 
B)  $\frac { 9 } { 13 }$ 
C)  $\frac { 21 } { 26 }$ 
D)  $\frac { 35 } { 52 }$

Question 11

Find the conditional probability.
-Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a diamond is selected
B = event a club is selected. Determine $\mathrm { P } ( \mathrm { A } \mid$ | (not $\mathrm { B } ) )$.

Accepted Answer

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

Question 12

In January in a certain city the unconditional probability of rain on any given day of the month is 0.400. But the probability of rain on a day that follows a rainy day is 0.600 and the probability of
Rain on a day following a nonrainy day is 0.250.
Find the probability that January 1st and January 2nd are rainy and that January 3rd and 4th are
Not rainy given that December 31st was clear all day.

Accepted Answer

A) 0.024 
B) 0.038 
C) 0.045 
D) 0.072 
A) 0.024 
B) 0.038 
C) 0.045 
D) 0.072

Question 13

Find the probability.
-Two 6-sided dice are rolled. What is the probability that the two numbers obtained differ by more than 2?

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 11 } { 36 }$ 
D)  $\frac { 13 } { 36 }$ 
A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 11 } { 36 }$ 
D)  $\frac { 13 } { 36 }$

Question 14

Mendel found that flower color in certain pea plants obeyed this scheme: Pure red crossed with pure white produces red. When pure red (RR)and pure white (rr)parents are crossed, the resulting Rr combination (one of Each gene)produces second generation offspring with red flowers, since red is dominant. Suppose One of these second generation Rr flowers is crossed with a pure red. What is the probability that The resulting plant will have red flowers?

Accepted Answer

A) 1 
B) 0.5 
C) 0.75 
D) 0.25 
A) 1 
B) 0.5 
C) 0.75 
D) 0.25

Question 15

Find the indicated probability.
-A fair die is rolled. Find the probability that the number obtained is not greater than 4.

Accepted Answer

A)  $\frac { 5 } { 6 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  $\frac { 5 } { 6 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $\frac { 1 } { 2 }$

Question 16

In January in a certain city the unconditional probability of rain on any given day of the month is 0.400. But the probability of rain on a day that follows a rainy day is 0.600 and the probability of
Rain on a day following a nonrainy day is 0.250. Find the probability of rain on three randomly
Selected consecutive days in January.

Accepted Answer

A) 0.144 
B) 0.090 
C) 0.064 
D) 0.216 
A) 0.144 
B) 0.090 
C) 0.064 
D) 0.216

Question 17

Decide whether or not the events are mutually exclusive.
-Events A and B defined as follows A card is drawn at random from a deck of cards. Event A is that the card obtained is a face card
And B is the event that the card obtained is a spade.

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 18

Find the indicated probability.
-If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

Accepted Answer

A)  $\frac { 31 } { 365 }$ 
B)  $\frac { 11 } { 12 }$ 
C)  $\frac { 31 } { 334 }$ 
D)  $\frac { 334 } { 365 }$ 
A)  $\frac { 31 } { 365 }$ 
B)  $\frac { 11 } { 12 }$ 
C)  $\frac { 31 } { 334 }$ 
D)  $\frac { 334 } { 365 }$

Question 19

Find the indicated probability.
-The age distribution of students at a community college is given below.   A student from the community college is selected at random. Find the probability that the student is at least 31. Round approximations to three decimal places.

Accepted Answer

A) 0.069 
B) 0.931 
C) 77 
D) 0.047 
A) 0.069 
B) 0.931 
C) 77 
D) 0.047

Question 20

Solve the problem.
- 
What are the odds against spinning a D on this spinner?

Accepted Answer

A)  $1 : 7$ 
B)  $7 : 1$ 
C)  $6 : 1$ 
D)  $8 : 1$ 
A)  $1 : 7$ 
B)  $7 : 1$ 
C)  $6 : 1$ 
D)  $8 : 1$

Find the indicated probability. -Two fair dice are rolled. Find the probability that the sum of the two numbers is not greater than 5.

Decide whether or not the events are mutually exclusive. -Events A and B defined as follows Event A is that at least three of Toni's five cousins are female. Event B is that at least three of Toni's five cousins are male.

Find the conditional probability. -If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is red, given that the first card was a heart.

Find the indicated probability. -The following table contains data from a study of two airlines which fly to Small Town, USA. If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight which was on time.

Two cards are selected without replacement from a standard deck of 52 cards. What is the probability that both cards are the same color (i.e., either both black or both red)?

Find the probability. -In one town, 70% of adults have health insurance. What is the probability that 8 adults selected at random from the town all have health insurance?

Find the conditional probability. -If three cards are drawn at random without replacement from a standard deck, find the probability that the third card is a face card, given that the first card was a queen and the second card was a 5.

Solve the problem. -The digits 1, 2, 3, 4, 5, and 7 are randomly arranged to form a six-digit number. Find the probability that the first and last digits are both even.

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In bridge, 4 aces

Find the indicated probability. -A card is drawn at random from a standard 52-card deck. Find the probability that the card is neither an ace nor a heart.

Find the conditional probability. -Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a diamond is selected B = event a club is selected. Determine $\mathrm { P } ( \mathrm { A } \mid$ | (not $\mathrm { B } ) )$ .

Find the probability. -Two 6-sided dice are rolled. What is the probability that the two numbers obtained differ by more than 2?

Find the indicated probability. -A fair die is rolled. Find the probability that the number obtained is not greater than 4.

Decide whether or not the events are mutually exclusive. -Events A and B defined as follows A card is drawn at random from a deck of cards. Event A is that the card obtained is a face card And B is the event that the card obtained is a spade.

Find the indicated probability. -If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

Find the indicated probability. -The age distribution of students at a community college is given below. A student from the community college is selected at random. Find the probability that the student is at least 31. Round approximations to three decimal places.

Solve the problem. - What are the odds against spinning a D on this spinner?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Exam 11: Probability

Find the indicated probability. -Two fair dice are rolled. Find the probability that the sum of the two numbers is not greater than 5.

Decide whether or not the events are mutually exclusive. -Events A and B defined as follows Event A is that at least three of Toni's five cousins are female. Event B is that at least three of Toni's five cousins are male.

Find the conditional probability. -If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is red, given that the first card was a heart.

Find the indicated probability. -The following table contains data from a study of two airlines which fly to Small Town, USA. If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight which was on time.

Two cards are selected without replacement from a standard deck of 52 cards. What is the probability that both cards are the same color (i.e., either both black or both red)?

Find the probability. -In one town, 70% of adults have health insurance. What is the probability that 8 adults selected at random from the town all have health insurance?

Find the conditional probability. -If three cards are drawn at random without replacement from a standard deck, find the probability that the third card is a face card, given that the first card was a queen and the second card was a 5.

Solve the problem. -The digits 1, 2, 3, 4, 5, and 7 are randomly arranged to form a six-digit number. Find the probability that the first and last digits are both even.

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In bridge, 4 aces

Find the indicated probability. -A card is drawn at random from a standard 52-card deck. Find the probability that the card is neither an ace nor a heart.

Find the conditional probability. -Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a diamond is selected B = event a club is selected. Determine P(A∣\mathrm { P } ( \mathrm { A } \midP(A∣ | (not B))\mathrm { B } ) )B)) .

Find the probability. -Two 6-sided dice are rolled. What is the probability that the two numbers obtained differ by more than 2?

Find the indicated probability. -A fair die is rolled. Find the probability that the number obtained is not greater than 4.

Decide whether or not the events are mutually exclusive. -Events A and B defined as follows A card is drawn at random from a deck of cards. Event A is that the card obtained is a face card And B is the event that the card obtained is a spade.

Find the indicated probability. -If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

Find the indicated probability. -The age distribution of students at a community college is given below. A student from the community college is selected at random. Find the probability that the student is at least 31. Round approximations to three decimal places.

Solve the problem. - What are the odds against spinning a D on this spinner?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Find the conditional probability. -Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a diamond is selected B = event a club is selected. Determine $\mathrm { P } ( \mathrm { A } \mid$ | (not $\mathrm { B } ) )$ .