Question 1

In a particular game of cards, success is measured by the number of aces drawn by each player. Eight cards are drawn by the first player. Given that the player is drawing from a full poker deck of 52 cards, find the probability that this player will draw two aces from the deck.

Accepted Answer

The answer of In a particular game of cards, success...

Question 2

An analyst estimates that a stock has the following probabilities of year-end prices.  a. Calculate the expected price at year-end.
B) Calculate the variance and the standard deviation.

Accepted Answer

The answer of An analyst estimates that a stock has...

Question 3

The following formula defines the ________ of a hypergeometric random variable
n    .

Accepted Answer

The answer of The following formula defines the ________ of...

Question 4

Suppose a baseball team has 14 players on the roster who are not members of the pitching staff. Of those 14 players, assume that three have recently taken a performance-enhancing drug. Suppose the league decides to randomly test five members of the team. What is the probability that exactly two of the tested players are found to have taken a performance-enhancing drug?

Accepted Answer

A)  0.2308 
B)  0.2473 
C)  0.4945 
D)  0.7692

Question 5

According to a study by the Centers for Disease Control and Prevention, about 33% of U.S. births are Caesarean deliveries. Suppose seven expectant mothers are randomly selected. The expected number of mothers who will not have a Caesarean delivery is ________.

Accepted Answer

A)  1.24 
B)  2.31 
C)  3.50 
D)  4.69

Question 6

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that none in a random sample of four calculators is defective?

Accepted Answer

A)  0.0010 
B)  0.2916 
C)  0.3439 
D)  0.6561

Question 7

The expected value of simple information is the mean of a discrete probability distribution when the discrete random variable is expressed in term of dollars.

Accepted Answer

A) True 
 B)False

Question 8

A six-sided, unfair (weighted) die has the following probability distribution.  Find the probability of rolling a 3 or less.

Accepted Answer

The answer of A six-sided, unfair (weighted) die has the...

Question 9

Consider the following discrete probability distribution.  What is the probability that X is greater than 0?

Accepted Answer

A)  0.10 
B)  0.35 
C)  0.55 
D)  0.65

Question 10

Which of the following can be represented by a continuous random variable?

Accepted Answer

A)  The time of a flight between Chicago and New York 
B)  The number of defective light bulbs in a sample of five 
C)  The number of arrivals to a drive-through bank window in a four-hour period 
D)  The score of a randomly selected student on a five-question multiple-choice quiz

Question 11

The number of cars sold by a car salesperson during each of the last 25 weeks is the following:  What is the probability that the salesperson sells no more than one car during a week?

Accepted Answer

A)  0.20 
B)  0.40 
C)  0.60 
D)  0.80

Question 12

An investor has a $200,000 portfolio of which $120,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table.  The correlation coefficient between the returns on Stocks A and B is ________.

Accepted Answer

A)  -0.17 
B)  0.20 
C)  0.80 
D)  4.97

Question 13

According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. What is the probability that one or more earthquakes with a magnitude of 6.5 or greater will strike the San Francisco Bay Area in the next year?

Accepted Answer

A)  0.0488 
B)  0.1353 
C)  0.4878 
D)  0.9512

Question 14

Which of the following is true about the hypergeometric distribution?

Accepted Answer

A)  The trials are independent and the probability of success may change from trial to trial. 
B)  The trials are independent and the probability of success does not change from trial to trial. 
C)  The trials are not independent and the probability of success may change from trial to trial. 
D)  The trials are not independent and the probability of success does not change from trial to trial.

Question 15

The number of homes sold by a realtor during a month has the following probability distribution:  What is the standard deviation of the number of homes sold by the realtor during a month?

Accepted Answer

A)  0.56 
B)  0.75 
C)  1 
D)  1.2

Question 16

A risk-loving consumer will take on risk even if the expected gain is negative.

Accepted Answer

A) True 
 B)False

Question 17

According to a Department of Labor report, the city of Detroit had a 20% unemployment rate in May. Eight working-age residents were chosen at random. What is the probability that exactly four residents were unemployed?

Accepted Answer

A)  0.0013 
B)  0.0091 
C)  0.0459 
D)  0.1468

Question 18

What is a characteristic of the mass function of a discrete random variable X?

Accepted Answer

A)  The sum of probabilities P(X = x) over all possible values x is 1. 
B)  For every possible value x, the probability P(X = x) is between 0 and 1. 
C)  Describes all possible values x with the associated probabilities P(X = x). 
D)  All of the above.

Question 19

You have inherited a lottery ticket that may be a $5,000 winner. You have a 35% chance of winning the $5,000 and a 65% chance of winning $0. You have an opportunity to sell the lottery ticket for $1,500. What is your expected return and what should you do if are risk neutral?

Accepted Answer

The answer of You have inherited a lottery ticket that...

Question 20

According to a Department of Labor report, the city of Detroit had a 20% unemployment rate in May. Eight working-age residents were chosen at random. What is the probability that at least two of the residents were unemployed?

Accepted Answer

A)  0.1678 
B)  0.3355 
C)  0.4967 
D)  0.5033

Exam 5: Discrete Probability Distributions

In a particular game of cards, success is measured by the number of aces drawn by each player. Eight cards are drawn by the first player. Given that the player is drawing from a full poker deck of 52 cards, find the probability that this player will draw two aces from the deck.

An analyst estimates that a stock has the following probabilities of year-end prices. a. Calculate the expected price at year-end. B) Calculate the variance and the standard deviation.

The following formula defines the ________ of a hypergeometric random variable n .

According to a study by the Centers for Disease Control and Prevention, about 33% of U.S. births are Caesarean deliveries. Suppose seven expectant mothers are randomly selected. The expected number of mothers who will not have a Caesarean delivery is ________.

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that none in a random sample of four calculators is defective?

The expected value of simple information is the mean of a discrete probability distribution when the discrete random variable is expressed in term of dollars.

A six-sided, unfair (weighted) die has the following probability distribution. Find the probability of rolling a 3 or less.

Consider the following discrete probability distribution. What is the probability that X is greater than 0?