Question 1

If you draw one card at random from a deck of 10 cards numbered 1 through 10, inclusive, what is the probability that the number you draw is divisible by 9? ​

Accepted Answer

A)  Pr(Divisible By 9) = 0 
B)  Pr(Divisible By 9) =   
C)  Pr(Divisible By 9) =   
D)  Pr(Divisible By 9) =   
E)  Pr(Divisible By 9) =   
A)  Pr(Divisible By 9) = 0 
B)  Pr(Divisible By 9) =   
C)  Pr(Divisible By 9) =   
D)  Pr(Divisible By 9) =   
E)  Pr(Divisible By 9) =

Question 2

In a certain city, the Democratic, Republican, and Consumer parties have members of their parties on the city council. The probability of a member of this party winning in any election depends on the proportional membership of his/her party at the time of the election. The probabilities for all these parties winning are given by the following transition matrix P. Using the given transition matrix and assuming the initial-probability vector is   , find the probability vectors for the next four steps of the Markov chain. Round all numerical values in your answer to four decimal places. ​   ​

Accepted Answer

A)    ,   ,   ,   
B)    ,   ,   ,   
C)    ,   ,   ,   
D)    ,   ,   ,   
E)    ,   ,   ,   
A)    ,   ,   ,   
B)    ,   ,   ,   
C)    ,   ,   ,   
D)    ,   ,   ,   
E)    ,   ,   ,

Question 3

Each of urns I and II has 2 red balls, 4 white balls, and 4 green balls. Urn III has 2 red balls, 5 white balls, and 3 green balls. An urn is selected at random and a ball is drawn. If the ball is green G, find the probability that urn III was selected. ​

Accepted Answer

Question 4

Each computer component that the Peggos Company produces is tested twice before it is shipped. There is a 0.7 probability that a defective component will be so identified by the first test and a 0.8 probability that it will be identified as being defective by the second test. What is the probability that a defective component will not be identified as defective before it is shipped? ​

Accepted Answer

A)  Pr(not identified) = 0.560 
B)  Pr(not identified) = 0.100 
C)  Pr(not identified) = 0.060 
D)  Pr(not identified) = 0.500 
E)  Pr(not identified) = 0.240 
A)  Pr(not identified) = 0.560 
B)  Pr(not identified) = 0.100 
C)  Pr(not identified) = 0.060 
D)  Pr(not identified) = 0.500 
E)  Pr(not identified) = 0.240

Question 5

Three balls are drawn, without replacement, from a bag containing 8 red balls and 6 white balls. Construct a probability tree to determine the probability that the third ball drawn is red R. ​

Accepted Answer

A)  Pr(third ball R) =   
B)  Pr(third ball R) =   
C)  Pr(third ball R) =   
D)  Pr(third ball R) =   
E)  Pr(third ball R) =   
A)  Pr(third ball R) =   
B)  Pr(third ball R) =   
C)  Pr(third ball R) =   
D)  Pr(third ball R) =   
E)  Pr(third ball R) =

Question 6

A bag contains 5 white balls and 5 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, the first ball is red R or the second is white W. ​

Accepted Answer

A)  Pr(R first ∪ W second) =   
B)  Pr(R first ∪ W second) = 1 
C)  Pr(R first ∪ W second) =   
D)  Pr(R first ∪ W second) =   
E)  Pr(R first ∪ W second) =   
A)  Pr(R first ∪ W second) =   
B)  Pr(R first ∪ W second) = 1 
C)  Pr(R first ∪ W second) =   
D)  Pr(R first ∪ W second) =   
E)  Pr(R first ∪ W second) =

Question 7

A small town has 8000 adult males and 6500 adult females. A sociologist conducted a survey and found that 40% of the males and 30% of the females drink heavily. An adult is selected at random from the town. What is the probability, rounded to four decimal places, that the person is male M, if it is known that the person drinks heavily DH? ​

Accepted Answer

Question 8

Suppose that five of the eight students running for class officers (president, vice president, secretary, and treasurer) have grade-point averages (GPAs) above 3.0. If the officers are selected at random, what is the probability that all four officers will be students with GPAs above 3.0? ​

Accepted Answer

A)  Pr(GPA > 3.0) =   
B)  Pr(GPA > 3.0) =   
C)  Pr(GPA > 3.0) =   
D)  Pr(GPA > 3.0) =   
E)  Pr(GPA > 3.0) =   
A)  Pr(GPA > 3.0) =   
B)  Pr(GPA > 3.0) =   
C)  Pr(GPA > 3.0) =   
D)  Pr(GPA > 3.0) =   
E)  Pr(GPA > 3.0) =

Question 9

If   , find n. ​

Accepted Answer

A)  24 
B)  22 
C)  120 
D)  529 
E)  115 
A)  24 
B)  22 
C)  120 
D)  529 
E)  115

Question 10

What is the probability of being dealt a poker hand of 5 cards containing exactly 5 cards of the same suit? Round your answer to six decimal places. ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

A bag contains 7 white balls and 3 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, both balls are red R. ​

Accepted Answer

A)  Pr(both R) =   
B)  Pr(both R) =   
C)  Pr(both R) =   
D)  Pr(both R) =   
E)  Pr(both R) =   
A)  Pr(both R) =   
B)  Pr(both R) =   
C)  Pr(both R) =   
D)  Pr(both R) =   
E)  Pr(both R) =

Question 12

From a deck of 52 ordinary playing cards, one card is drawn. What is the probability that it is a spade(S)? ​

Accepted Answer

A)  Pr(S) =   
B)  Pr(S) =   
C)  Pr(S) =   
D)  Pr(S) =   
E)  Pr(S) =   
A)  Pr(S) =   
B)  Pr(S) =   
C)  Pr(S) =   
D)  Pr(S) =   
E)  Pr(S) =

Question 13

A ball is drawn from a bag containing 14 red balls numbered 1-14 and 11 white balls numbered 15-25. What is the probability that the ball is red R or even-numbered E? ​

Accepted Answer

A)  Pr(R∪
E)  =   
B)  Pr(R∪
E)  =   
C)  Pr(R∪
E)  =   
D)  Pr(R∪
E)  =   
E)  Pr(R∪
E)  =   
A)  Pr(R∪
E)  =   
B)  Pr(R∪
E)  =   
C)  Pr(R∪
E)  =   
D)  Pr(R∪
E)  =   
E)  Pr(R∪
E)  =

Question 14

One ball is drawn at random from a bag containing 6 red R balls and 10 white W balls. What is the probability that the ball is red or white? ​

Accepted Answer

A)    
B)    
C)    
D)  ​   
E)    
A)    
B)    
C)    
D)  ​   
E)

Question 15

Of 100 students, 26 can speak French F, 33 can speak German G, and 16 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German? ​

Accepted Answer

A)  Pr(F∪G) =   
B)  Pr(F∪G) =   
C)  Pr(F∪G) =   
D)  Pr(F∪G) =   
E)  Pr(F∪G) =   
A)  Pr(F∪G) =   
B)  Pr(F∪G) =   
C)  Pr(F∪G) =   
D)  Pr(F∪G) =   
E)  Pr(F∪G) =

Question 16

A bag contains 9 white balls and 5 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that all three balls are white W. ​

Accepted Answer

A)  Pr(three W) =   
B)  Pr(three W) =   
C)  Pr(three W) =   
D)  Pr(three W) =   
E)  Pr(three W) =   
A)  Pr(three W) =   
B)  Pr(three W) =   
C)  Pr(three W) =   
D)  Pr(three W) =   
E)  Pr(three W) =

Question 17

A bag contains 7 red balls numbered 1-7 and 15 white balls numbered 8-22. One ball is drawn from the bag. What is the probability that the ball is red R, given that the ball is even-numbered E? ​

Accepted Answer

Question 18

A ball is drawn from a bag containing 8 red balls numbered 1-8 and 7 white balls numbered 9-15. What is the probability that the ball is neither red R nor even-numbered E? ​

Accepted Answer

A)  Pr(R'∩E') =   
B)  Pr(R'∩E') =   
C)  Pr(R'∩E') =   
D)  Pr(R'∩E') =   
E)  Pr(R'∩E') =   
A)  Pr(R'∩E') =   
B)  Pr(R'∩E') =   
C)  Pr(R'∩E') =   
D)  Pr(R'∩E') =   
E)  Pr(R'∩E') =

Question 19

A car dealer has 15 different cars that he would like to display, but he has room to display only 5. Suppose 9 of the cars are the same color, with the remaining 6 having different colors that are distinct from each other. If the dealer tells a salesperson to display any 5 cars, what is the probability that all 5 cars will be the same color? ​

Accepted Answer

A)  Pr(All Same Color) =   
B)  Pr(All Same Color) =   
C)  Pr(All Same Color) =   
D)  Pr(All Same Color) =   
E)  Pr(All Same Color) =   
A)  Pr(All Same Color) =   
B)  Pr(All Same Color) =   
C)  Pr(All Same Color) =   
D)  Pr(All Same Color) =   
E)  Pr(All Same Color) =

Question 20

An ordinary die is tossed. What is the probability of getting an even number or a number divisible by 6? ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

If you draw one card at random from a deck of 10 cards numbered 1 through 10, inclusive, what is the probability that the number you draw is divisible by 9?

Each of urns I and II has 2 red balls, 4 white balls, and 4 green balls. Urn III has 2 red balls, 5 white balls, and 3 green balls. An urn is selected at random and a ball is drawn. If the ball is green G, find the probability that urn III was selected.

Three balls are drawn, without replacement, from a bag containing 8 red balls and 6 white balls. Construct a probability tree to determine the probability that the third ball drawn is red R.

A bag contains 5 white balls and 5 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, the first ball is red R or the second is white W.

Suppose that five of the eight students running for class officers (president, vice president, secretary, and treasurer) have grade-point averages (GPAs) above 3.0. If the officers are selected at random, what is the probability that all four officers will be students with GPAs above 3.0?

If , find n.

What is the probability of being dealt a poker hand of 5 cards containing exactly 5 cards of the same suit? Round your answer to six decimal places.

A bag contains 7 white balls and 3 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, both balls are red R.

From a deck of 52 ordinary playing cards, one card is drawn. What is the probability that it is a spade(S)?

A ball is drawn from a bag containing 14 red balls numbered 1-14 and 11 white balls numbered 15-25. What is the probability that the ball is red R or even-numbered E?

One ball is drawn at random from a bag containing 6 red R balls and 10 white W balls. What is the probability that the ball is red or white?

Of 100 students, 26 can speak French F, 33 can speak German G, and 16 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German?

A bag contains 9 white balls and 5 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that all three balls are white W.

A bag contains 7 red balls numbered 1-7 and 15 white balls numbered 8-22. One ball is drawn from the bag. What is the probability that the ball is red R, given that the ball is even-numbered E?

A ball is drawn from a bag containing 8 red balls numbered 1-8 and 7 white balls numbered 9-15. What is the probability that the ball is neither red R nor even-numbered E?

An ordinary die is tossed. What is the probability of getting an even number or a number divisible by 6?

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Exam 7: Introduction to Probability

If you draw one card at random from a deck of 10 cards numbered 1 through 10, inclusive, what is the probability that the number you draw is divisible by 9? ​

Each of urns I and II has 2 red balls, 4 white balls, and 4 green balls. Urn III has 2 red balls, 5 white balls, and 3 green balls. An urn is selected at random and a ball is drawn. If the ball is green G, find the probability that urn III was selected. ​

Three balls are drawn, without replacement, from a bag containing 8 red balls and 6 white balls. Construct a probability tree to determine the probability that the third ball drawn is red R. ​

A bag contains 5 white balls and 5 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, the first ball is red R or the second is white W. ​

Suppose that five of the eight students running for class officers (president, vice president, secretary, and treasurer) have grade-point averages (GPAs) above 3.0. If the officers are selected at random, what is the probability that all four officers will be students with GPAs above 3.0? ​

If , find n. ​

What is the probability of being dealt a poker hand of 5 cards containing exactly 5 cards of the same suit? Round your answer to six decimal places. ​

A bag contains 7 white balls and 3 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, both balls are red R. ​

From a deck of 52 ordinary playing cards, one card is drawn. What is the probability that it is a spade(S)? ​

A ball is drawn from a bag containing 14 red balls numbered 1-14 and 11 white balls numbered 15-25. What is the probability that the ball is red R or even-numbered E? ​

One ball is drawn at random from a bag containing 6 red R balls and 10 white W balls. What is the probability that the ball is red or white? ​

Of 100 students, 26 can speak French F, 33 can speak German G, and 16 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German? ​

A bag contains 9 white balls and 5 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that all three balls are white W. ​

A bag contains 7 red balls numbered 1-7 and 15 white balls numbered 8-22. One ball is drawn from the bag. What is the probability that the ball is red R, given that the ball is even-numbered E? ​

A ball is drawn from a bag containing 8 red balls numbered 1-8 and 7 white balls numbered 9-15. What is the probability that the ball is neither red R nor even-numbered E? ​

An ordinary die is tossed. What is the probability of getting an even number or a number divisible by 6? ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

If you draw one card at random from a deck of 10 cards numbered 1 through 10, inclusive, what is the probability that the number you draw is divisible by 9?

Each of urns I and II has 2 red balls, 4 white balls, and 4 green balls. Urn III has 2 red balls, 5 white balls, and 3 green balls. An urn is selected at random and a ball is drawn. If the ball is green G, find the probability that urn III was selected.

Three balls are drawn, without replacement, from a bag containing 8 red balls and 6 white balls. Construct a probability tree to determine the probability that the third ball drawn is red R.

A bag contains 5 white balls and 5 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, the first ball is red R or the second is white W.

Suppose that five of the eight students running for class officers (president, vice president, secretary, and treasurer) have grade-point averages (GPAs) above 3.0. If the officers are selected at random, what is the probability that all four officers will be students with GPAs above 3.0?

If , find n.

What is the probability of being dealt a poker hand of 5 cards containing exactly 5 cards of the same suit? Round your answer to six decimal places.

A bag contains 7 white balls and 3 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, both balls are red R.

From a deck of 52 ordinary playing cards, one card is drawn. What is the probability that it is a spade(S)?

A ball is drawn from a bag containing 14 red balls numbered 1-14 and 11 white balls numbered 15-25. What is the probability that the ball is red R or even-numbered E?

One ball is drawn at random from a bag containing 6 red R balls and 10 white W balls. What is the probability that the ball is red or white?

Of 100 students, 26 can speak French F, 33 can speak German G, and 16 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German?

A bag contains 9 white balls and 5 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that all three balls are white W.

A bag contains 7 red balls numbered 1-7 and 15 white balls numbered 8-22. One ball is drawn from the bag. What is the probability that the ball is red R, given that the ball is even-numbered E?

A ball is drawn from a bag containing 8 red balls numbered 1-8 and 7 white balls numbered 9-15. What is the probability that the ball is neither red R nor even-numbered E?

An ordinary die is tossed. What is the probability of getting an even number or a number divisible by 6?