Question 1

Compute  .

Accepted Answer

A) 0 
B) 1 
C) 3 
D) 9 
E) 27

Question 2

Suppose that a marksman hits the bull's-eye 1 time in 10 shots. If the next 4 shots are independent, find the probability that exactly two of the next 4 shots hit the bull's-eye. ​

Accepted Answer

A) Pr(two bull's-eyes) =  
B) Pr(two bull's-eyes) =  
C) Pr(two bull's-eyes) =  
D) Pr(two bull's-eyes) =  
E) Pr(two bull's-eyes) =

Question 3

An ordinary die is tossed. What is the probability of getting a 6 or a 5? ​

Accepted Answer

A) Pr(3 or 4) =  
B) Pr(3 or 4) =  
C) Pr(3 or 4) =  
D) Pr(3 or 4) =  
E) Pr(3 or 4) = 1

Question 4

Three balls are drawn, without replacement, from a bag containing 9 red balls and 7 white balls. Construct a probability tree to determine the probability that two white W balls and one red R ball are drawn in any order. ​

Accepted Answer

A) Pr(two W ∩ one R) =  
B) Pr(two W ∩ one R) =  
C) Pr(two W ∩ one R) =  
D) Pr(two W ∩ one R) =  
E) Pr(two W ∩ one R) =

Question 5

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') =

Question 6

A senator asks his constituents to rank seven issues in order of importance. What is the probability that one reply chosen at random will rank the issues in alphabetical order? ​

Accepted Answer

A) Pr(Alphabetical Order) =  
B) Pr(Alphabetical Order) =  
C) Pr(Alphabetical Order) =  
D) Pr(Alphabetical Order) =  
E) Pr(Alphabetical Order) =

Question 7

In a sales promotion, a clothing store gives its customers a chance to draw a ticket from a box that contains a discount on their next purchase. The box contains 9000 tickets giving a 10% discount, 900 giving a 30% discount, 450 giving a 50% discount, and 4 giving a 100% discount. What is the probability that a given customer will randomly draw a ticket giving a 50% discount? ​

Accepted Answer

A) Pr(50%) =  
B) Pr(50%) =  
C) Pr(50%) =  
D) Pr(50%) =  
E) Pr(50%) =

Question 8

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 9

To determine voters' feelings regarding an issue, a candidate asks a sample of people to pick 5 words out of a set of 6 words that they feel best describe the issue. How many different groupings of 5 words are possible? ​

Accepted Answer

A) 121 
B) 30 
C) 7,776 
D) 720 
E) 6

Question 10

A bag contains 5 coins, of which 4 are fair; the remaining coin has a head on both sides. If a coin is selected at random from the bag and tossed three times, construct a probability tree to determine the probability that heads will occur at least twice. ​

Accepted Answer

A) Pr(at least two heads) =  
B) Pr(at least two heads) =  
C) Pr(at least two heads) =  
D) Pr(at least two heads) =  
E) Pr(at least two heads) =

Question 11

Thirty-seven percent of the cars owned by a car rental firm have some defect. What is the probability that if 3 cars are selected at random, at least one would have a defect? Round your answer to four decimal places. ​

Accepted Answer

A) 0.0507 
B) 0.2500 
C) 0.7500 
D) 0.6031 
E) 0.8425

Question 12

Lactose intolerance affects about 10% of non-Hispanic white Americans, 50% of Hispanic Americans, and 70% of African, Asian, and Native Americans. Seventy-four percent of U.S. residents are non-Hispanic whites, 10% of them are Hispanic, and 11% are African, Asian, or Native American. If a person is selected from this group of people, what is the probability, to four decimal places, that the person will be lactose intolerant? ​

Accepted Answer

A) Pr(lactose intolerant) = 0.1240 
B) Pr(lactose intolerant) = 0.2010 
C) Pr(lactose intolerant) = 0.1270 
D) Pr(lactose intolerant) = 0.1510 
E) Pr(lactose intolerant) = 0.1310

Question 13

A sailboat owner received 9 different signal flags with his new sailboat. If the order in which the flags are arranged on the mast determines the signal being sent, how many 4-flag signals can be sent? ​

Accepted Answer

A) 151,200 
B) 30,240 
C) 13 
D) 36 
E) 3,024

Question 14

A bag contains 9 white balls W and 9 red balls R. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that at least one white W ball is drawn. ​

Accepted Answer

A) Pr(at least one W) =  
B) Pr(at least one W) =  
C) Pr(at least one W) =  
D) Pr(at least one W) =  
E) Pr(at least one W) =

Question 15

Compute  . ​

Accepted Answer

A) 6 
B) 13,949 
C) 6,970 
D) 167 
E) 98,770

Question 16

In a 10-question matching test with 10 possible answers to match and no answer used more than once, what is the probability of guessing and getting every answer correct? ​

Accepted Answer

A) Pr(All Correct) =  
B) Pr(All Correct) =  
C) Pr(All Correct) =  
D) Pr(All Correct) =  
E) Pr(All Correct) =

Question 17

Can the matrix  be a transition matrix?

Accepted Answer

A) Yes 
B) No

Question 18

An automatic teller machine requires that each customer enter a three-digit personal identification number (PIN) when he or she inserts a bank card. If a person finds a bank card and guesses at a PIN to use the card fraudulently, what is the probability that the person will succeed in one attempt? ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate two of the possible answers on the first five questions, and if she guesses on every question, what is the probability that she will answer at least one question correctly? ​

Accepted Answer

A) Pr(at least 1 correct) =  
B) Pr(at least 1 correct) =  
C) Pr(at least 1 correct) =  
D) Pr(at least 1 correct) =  
E) Pr(at least 1 correct) =

Question 20

Can the vector  be a probability vector?

Accepted Answer

A) Yes 
B) No

Exam 8: Introduction to Probability

Compute .

Suppose that a marksman hits the bull's-eye 1 time in 10 shots. If the next 4 shots are independent, find the probability that exactly two of the next 4 shots hit the bull's-eye. ​

An ordinary die is tossed. What is the probability of getting a 6 or a 5? ​

Three balls are drawn, without replacement, from a bag containing 9 red balls and 7 white balls. Construct a probability tree to determine the probability that two white W balls and one red R ball are drawn in any order. ​

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? ​

A senator asks his constituents to rank seven issues in order of importance. What is the probability that one reply chosen at random will rank the issues in alphabetical order? ​

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? ​

To determine voters' feelings regarding an issue, a candidate asks a sample of people to pick 5 words out of a set of 6 words that they feel best describe the issue. How many different groupings of 5 words are possible? ​

A bag contains 5 coins, of which 4 are fair; the remaining coin has a head on both sides. If a coin is selected at random from the bag and tossed three times, construct a probability tree to determine the probability that heads will occur at least twice. ​

Thirty-seven percent of the cars owned by a car rental firm have some defect. What is the probability that if 3 cars are selected at random, at least one would have a defect? Round your answer to four decimal places. ​

A sailboat owner received 9 different signal flags with his new sailboat. If the order in which the flags are arranged on the mast determines the signal being sent, how many 4-flag signals can be sent? ​

A bag contains 9 white balls W and 9 red balls R. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that at least one white W ball is drawn. ​

Compute . ​

In a 10-question matching test with 10 possible answers to match and no answer used more than once, what is the probability of guessing and getting every answer correct? ​

Can the matrix be a transition matrix?

Can the vector be a probability vector?

Suppose that a marksman hits the bull's-eye 1 time in 10 shots. If the next 4 shots are independent, find the probability that exactly two of the next 4 shots hit the bull's-eye.

An ordinary die is tossed. What is the probability of getting a 6 or a 5?

Three balls are drawn, without replacement, from a bag containing 9 red balls and 7 white balls. Construct a probability tree to determine the probability that two white W balls and one red R ball are drawn in any order.

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?

A senator asks his constituents to rank seven issues in order of importance. What is the probability that one reply chosen at random will rank the issues in alphabetical order?

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?

To determine voters' feelings regarding an issue, a candidate asks a sample of people to pick 5 words out of a set of 6 words that they feel best describe the issue. How many different groupings of 5 words are possible?

A bag contains 5 coins, of which 4 are fair; the remaining coin has a head on both sides. If a coin is selected at random from the bag and tossed three times, construct a probability tree to determine the probability that heads will occur at least twice.

Thirty-seven percent of the cars owned by a car rental firm have some defect. What is the probability that if 3 cars are selected at random, at least one would have a defect? Round your answer to four decimal places.

A sailboat owner received 9 different signal flags with his new sailboat. If the order in which the flags are arranged on the mast determines the signal being sent, how many 4-flag signals can be sent?

A bag contains 9 white balls W and 9 red balls R. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that at least one white W ball is drawn.

Compute .

In a 10-question matching test with 10 possible answers to match and no answer used more than once, what is the probability of guessing and getting every answer correct?