Question 1

A ball is drawn from a bag containing 6 red balls numbered 1-6 and 14 white balls numbered 7-20. What is the probability that the ball is not red R? ​

Accepted Answer

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

Question 2

Suppose that all license plates in a state have three of the letters A through Z followed by four of the digits 0 through 9. If a plate is chosen at random, what is the probability that all three letters and all four digits on the plate will be different? Round your answer to five decimal places. ​

Accepted Answer

A)  0.018639 
B)  0.074556 
C)  0.447337 
D)  0.546000 
E)  0.080769

Question 3

A game of cards is played with a hand that consists of 3 cards dealt from a deck of 46 cards. How many different hands of cards are possible? ​

Accepted Answer

A)  15,180 
B)  91,080 
C)  138 
D)  97,336 
E)  6,348

Question 4

Three balls are drawn, without replacement, from a bag containing 9 red balls and 4 white balls. Construct a probability tree to determine the probability that three white W balls are drawn. ​

Accepted Answer

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

Question 5

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 6

If the probability that an event will occur is  , what are the odds in favor of the event occurring? ​

Accepted Answer

A)  9 : 2 
B)  2 : 9 
C)  11 : 2 
D)  2 : 11 
E)  9 : 11

Question 7

A red ball and 18 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 white W balls? ​

Accepted Answer

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

Question 8

Assuming there are 365 different birthdays, find the probability that at least two of nine people chosen at random will have same birthdays. Round your answer to five decimal places. ​

Accepted Answer

A)  0.04895 
B)  0.00538 
C)  0.81075 
D)  0.54731 
E)  0.09462

Question 9

An automatic teller machine requires that each customer enter a five-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, and the person knows that the PIN will not have any digit repeated, what is the probability the person will succeed in guessing in one attempt? ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

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 11

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places. ​

Accepted Answer

A)  0.97736 
B)  0.84986 
C)  0.87286 
D)  0.48643 
E)  0.97286

Question 12

A car dealer has 7 different cars that he would like to display, but he has room to display only 4. In how many ways can he pick 4 cars to display? ​

Accepted Answer

A)  840 
B)  165 
C)  121 
D)  35 
E)  28

Question 13

A ball is drawn from a bag containing 15 red balls numbered 1-15 and 6 white balls numbered 16-21. What is the probability that the ball is red R and 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 14

Suppose the following table summarizes the opinions of various groups on the issue of increased military spending. ​

Given that a randomly selected individual is nonwhite NW, find the probability that he or she opposes increased military spending O.
​

Accepted Answer

Question 15

Can the matrix  be a transition matrix?

Accepted Answer

A) True 
 B)False

Question 16

If the first digit of a seven-digit telephone number cannot be a 0 or 1, what is the probability that a number chosen at random will have all seven digits the same? ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

The following table gives the average number of voters in each of three political parties during the last 12 years, along with the average number that voted in presidential elections during this period. Use these data to find the probability, rounded to two decimal places, that a person selected at random from the registered Democratic voters will vote in the next election. ​

Accepted Answer

A)  Pr(Democratic will vote) = 0.55 
B)  Pr(Democratic will vote) = 0.44 
C)  Pr(Democratic will vote) = 0.24 
D)  Pr(Democratic will vote) = 0.56 
E)  Pr(Democratic will vote) = 0.45

Question 18

An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate 1 of the possible answers on the first 5 questions, and if she guesses on every question, what is the probability that she will answer every question incorrectly? ​

Accepted Answer

A)  Pr(all incorrect) =  
B)  Pr(all incorrect) =  
C)  Pr(all incorrect) =  
D)  Pr(all incorrect) =  
E)  Pr(all incorrect) =

Question 19

A Markov chain has transition matrix  and initial-probability vector  . Find the probability vector for the third stage of the Markov chain. ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

A self-administered pregnancy test detects 80% of those who are pregnant but does not detect pregnancy in 20%. It is 92% accurate in indicating women who are not pregnant but indicates 8% of this group as being pregnant. Suppose it is known that 2% of the women in a neighborhood are pregnant. If a woman is chosen at random from those living in this neighborhood, and if the test indicates she is pregnant, what is the probability, rounded to four decimal places, that she really is? ​

Accepted Answer

Exam 7: Introduction to Probability

A ball is drawn from a bag containing 6 red balls numbered 1-6 and 14 white balls numbered 7-20. What is the probability that the ball is not red R?

Suppose that all license plates in a state have three of the letters A through Z followed by four of the digits 0 through 9. If a plate is chosen at random, what is the probability that all three letters and all four digits on the plate will be different? Round your answer to five decimal places.

A game of cards is played with a hand that consists of 3 cards dealt from a deck of 46 cards. How many different hands of cards are possible?

Three balls are drawn, without replacement, from a bag containing 9 red balls and 4 white balls. Construct a probability tree to determine the probability that three white W balls are drawn.

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.

If the probability that an event will occur is , what are the odds in favor of the event occurring?

A red ball and 18 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 white W balls?

Assuming there are 365 different birthdays, find the probability that at least two of nine people chosen at random will have same birthdays. Round your answer to five decimal places.

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?

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places.

A car dealer has 7 different cars that he would like to display, but he has room to display only 4. In how many ways can he pick 4 cars to display?

A ball is drawn from a bag containing 15 red balls numbered 1-15 and 6 white balls numbered 16-21. What is the probability that the ball is red R and even-numbered E?

Suppose the following table summarizes the opinions of various groups on the issue of increased military spending. Given that a randomly selected individual is nonwhite NW, find the probability that he or she opposes increased military spending O.

Can the matrix be a transition matrix?

If the first digit of a seven-digit telephone number cannot be a 0 or 1, what is the probability that a number chosen at random will have all seven digits the same?

An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate 1 of the possible answers on the first 5 questions, and if she guesses on every question, what is the probability that she will answer every question incorrectly?

A Markov chain has transition matrix and initial-probability vector . Find the probability vector for the third stage of the Markov chain.

Exam 7: Introduction to Probability

A ball is drawn from a bag containing 6 red balls numbered 1-6 and 14 white balls numbered 7-20. What is the probability that the ball is not red R? ​

A game of cards is played with a hand that consists of 3 cards dealt from a deck of 46 cards. How many different hands of cards are possible? ​

Three balls are drawn, without replacement, from a bag containing 9 red balls and 4 white balls. Construct a probability tree to determine the probability that three white W balls are drawn. ​

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. ​

If the probability that an event will occur is , what are the odds in favor of the event occurring? ​

A red ball and 18 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 white W balls? ​

Assuming there are 365 different birthdays, find the probability that at least two of nine people chosen at random will have same birthdays. Round your answer to five decimal places. ​

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? ​

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places. ​

A car dealer has 7 different cars that he would like to display, but he has room to display only 4. In how many ways can he pick 4 cars to display? ​

A ball is drawn from a bag containing 15 red balls numbered 1-15 and 6 white balls numbered 16-21. What is the probability that the ball is red R and even-numbered E? ​

Suppose the following table summarizes the opinions of various groups on the issue of increased military spending. ​ Given that a randomly selected individual is nonwhite NW, find the probability that he or she opposes increased military spending O. ​

Can the matrix be a transition matrix?

If the first digit of a seven-digit telephone number cannot be a 0 or 1, what is the probability that a number chosen at random will have all seven digits the same? ​

A Markov chain has transition matrix and initial-probability vector . Find the probability vector for the third stage of the Markov chain. ​

A ball is drawn from a bag containing 6 red balls numbered 1-6 and 14 white balls numbered 7-20. What is the probability that the ball is not red R?

A game of cards is played with a hand that consists of 3 cards dealt from a deck of 46 cards. How many different hands of cards are possible?

Three balls are drawn, without replacement, from a bag containing 9 red balls and 4 white balls. Construct a probability tree to determine the probability that three white W balls are drawn.

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.

If the probability that an event will occur is , what are the odds in favor of the event occurring?

A red ball and 18 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting 2 white W balls?

Assuming there are 365 different birthdays, find the probability that at least two of nine people chosen at random will have same birthdays. Round your answer to five decimal places.

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?

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places.

A car dealer has 7 different cars that he would like to display, but he has room to display only 4. In how many ways can he pick 4 cars to display?

A ball is drawn from a bag containing 15 red balls numbered 1-15 and 6 white balls numbered 16-21. What is the probability that the ball is red R and even-numbered E?

Suppose the following table summarizes the opinions of various groups on the issue of increased military spending. Given that a randomly selected individual is nonwhite NW, find the probability that he or she opposes increased military spending O.

If the first digit of a seven-digit telephone number cannot be a 0 or 1, what is the probability that a number chosen at random will have all seven digits the same?

A Markov chain has transition matrix and initial-probability vector . Find the probability vector for the third stage of the Markov chain.