Deck 4: Probability and Probability Distributions

Question 1

Probability is a number between 0 and 1, inclusive, which measures the likelihood that some event will occur.

Answer 1

True

Question 2

If P(A) = 0.25 and P(B) = 0.65, then P(A and B) is:

A) 0.25
B) 0.40
C) 0.90
D) This cannot be determined from the information given.

Answer 2

This cannot be determined from the information given.

Question 3

Which of the following best describes the concept of probability?

A) It is a measure of the likelihood that a particular event will occur.
B) It is a measure of the likelihood that a particular event will occur, given that another event has already occurred.
C) It is a measure of the likelihood of the simultaneous occurrence of two or more events.
D) None of these choices describe the concept of probability.

Answer 3

It is a measure of the likelihood that a particular event will occur.

Question 4

If two events are mutually exclusive, what is the probability that both occur at the same time?

A) 0.00
B) 0.50
C) 1.00
D) This cannot be determined from the information given.

Question 5

The probabilities shown in a table with two rows, and and two columns, and , are as follows: P( and ) = .10, P( and ) = .30, P( and ) = .05, and P( and ) = .55. Then P( | ), calculated up to two decimals, is:

A) .33
B) .35
C) .65
D) .67

Question 6

If events A and B have nonzero probabilities, then they can be both independent and mutually exclusive.

Question 7

The law of large numbers is relevant to the estimation of:

A) objective probabilities
B) subjective probabilities
C) both objective and subjective probabilities
D) neither objective nor subjective probabilities

Question 8

If events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal to:

A) 0.0
B) 0.5
C) 1.0
D) any value between 0.5 and 1.0

Question 9

Two or more events are said to be exhaustive if one of them must occur.

Question 10

If P(A and B) = 1, then A and B must be collectively exhaustive.

Question 11

Let A and B be the events of the FDA approving and rejecting a new drug to treat hypertension, respectively. The events A and B are:

A) independent
B) conditional
C) unilateral
D) mutually exclusive

Question 12

The probabilities shown in a table with two rows, and and two columns, and , are as follows: P( and ) = .10, P( and ) = .30, P( and ) = .05, and P( and ) = .55. Then P( | ), calculated up to two decimals, is:

A) .33
B) .35
C) .65
D) .67

Question 13

If A and B are independent events with P(A) = 0.40 and P(B) = 0.50, then P(A/B) is 0.50.

Question 14

If two events are collectively exhaustive, what is the probability that both occur at the same time?

A) 0.00
B) 0.50
C) 1.00
D) This cannot be determined from the information given.

Question 15

If P(A) = P(A|B), then events A and B are said to be:

A) mutually exclusive
B) independent
C) exhaustive
D) complementary

Question 16

A function that associates a numerical value with each possible outcome of an uncertain event is called a:

A) conditional variable
B) random variable
C) population variable
D) sample variable

Question 17

If A and B are mutually exclusive events with P(A) = 0.70, then P(B):

A) can be any value between 0 and 1
B) can be any value between 0 and 0.70
C) cannot be larger than 0.30
D) can be any value between 0.30 and 0.70

Question 18

If two events are independent, what is the probability that they both occur?

A) 0
B) 0.50
C) 1.00
D) This cannot be determined from the information given.

Question 19

If A and B are any two events with P(A) = .8 and P(B|A) = .4, then the joint probability of A and B is:

A) .80
B) .40
C) .32
D) 1.20

Question 20

You think you have a 90% chance of passing your statistics class. This is an example of subjective probability.

Question 21

Two events A and B are said to mutually be exclusive if P(A and B) = 0.

Question 22

Football teams toss a coin to see who will get their choice of kicking or receiving to begin a game. The probability that given team will win the toss three games in a row is 0.125.

Question 23

Two or more events are said to be mutually exclusive if at most one of them can occur.

Question 24

How many females were interviewed?

Question 25

The law of large numbers states that subjective probabilities can be estimated based on the long run relative frequencies of events.

Question 26

The multiplication rule for two events A and B is: P(A and B) = P(A|B)P(A).

Question 27

What is the probability that a respondent chosen at random is a male?

Question 28

Two or more events are said to be exhaustive if at most one of them can occur.

Question 29

Two events are said to be independent when knowledge of one event is of no value when assessing the probability of the other.

Question 30

The relative frequency of an event is the number of times the event occurs out of the total number of times the random experiment is run.

Question 31

Suppose that after graduation, you will either buy a new car (event A) or take a trip to Europe (event B). In this case, events A and B are mutually exclusive.

Question 32

Conditional probability is the probability that an event will occur, with no other events taken into consideration.

Question 33

If A and B are two independent events with P(A) = 0.20 and P(B) = 0.60, then P(A and B) = 0.80.

Question 34

What is the probability that a respondent chosen at random enjoys shopping for clothing?

Question 35

Suppose A and B are mutually exclusive events where P(A) = 0.3 and P(B) = 0.4. Then, P(A and B) = 0.12.

Question 36

What is the probability that a household answered no?

Question 37

Suppose A and B are two events where P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.2, then P(B/A) = 0.5.

Question 38

Given that events A and B are independent and that P(A) = 0.8 and P(B/A) = 0.4, then P(A and B) = 0.32.

Question 39

What is the probability that a respondent was female?

Question 40

If P(A and B) = 0, then A and B must be collectively exhaustive.

Question 41

What is the probability that a respondent chosen at random is a male who enjoys shopping for clothing or a female who enjoys shopping for clothing?

Question 42

Are gender of patrons and drinking preference independent? Explain.

Question 43

What is the probability that a respondent chosen at random is a male and does not enjoy shopping for clothing?

Question 44

What is the probability that a respondent chosen at random enjoys or does not enjoy shopping for clothing?

Question 45

What is the probability that none of the oil wells will be successful?

Question 46

Suppose a randomly selected patron prefers beer. What is the probability the patron is a male?

Question 47

Suppose a randomly selected patron prefers wine. What is the probability the patron is a male?

Question 48

What is the probability that a respondent chosen at random is a female and does not enjoy shopping for clothing?

Question 49

Suppose a randomly selected patron is a female. What is the probability that the patron prefers wine?

Question 50

What is the probability that any well will not be successful?

Question 51

What is the probability that a respondent chosen at random does not enjoy shopping for clothing?

Question 52

Does consumer behavior depend on the gender of consumer? Explain using probabilities.

Question 53

What is the probability a randomly selected patron prefers wine?

Question 54

What is the probability a randomly selected patron is a female who prefers beer?

Question 55

Suppose a randomly selected patron is a female. What is the probability the patron prefers beer?

Question 56

What is the probability a randomly selected patron is a female who prefers wine?

Question 57

What is the probability that a respondent chosen at random is a male or a female?

Question 58

What is the probability that a randomly selected patron is not male?

Question 59

What is the probability a randomly selected patron is a female?

Question 60

What is the probability that a respondent chosen at random is a female and enjoys shopping for clothing?

Question 61

​A probability tree is a graphical representation of how events occur through time, which is useful for calculating probabilities.

Question 62

Find the probability that three or fewer customers are in line.

Question 63

If it costs $200,000 to drill each well and a successful well will produce $1,000,000 worth of oil over its lifetime, what is the expected net value of this three-well program if no wells are successful?

Question 64

The time students spend in a computer lab during one day is an example of a continuous random variable.

Question 65

If it costs $200,000 to drill each well and a successful well will produce $1,000,000 worth of oil over its lifetime, what is the expected net value of this three-well program if all three wells are successful?

Question 66

There are two types of random variables, they are:

A) discrete and continuous
B) exhaustive and mutually exclusive
C) complementary and cumulative
D) real and unreal

Question 67

A discrete probability distribution:

A) is a set of possible values and a corresponding set of probabilities that sum to 1
B) is a modeling tool that can be used to incorporate uncertainty into models
C) can be estimated from long-run proportions
D) is the distribution of a single random variable

Question 68

(A) What is the expected completion time (in months) from now for this project?
(B) How much variability (in months) exists around the expected value found in (A)?

Question 69

Find the probability distribution of X.

Question 70

What is the probability that this project will be completed in less than 4 months from now?

Question 71

A small grocery store is considering installing an express checkout line. Let X be the number of customers in the regular checkout line. Note that these numbers include the customers being served, if any. The probability distribution of X is given in the table below.
Find the probability that no more than one customer is in line.

Question 72

The number of cars produced by GM during a given quarter is a continuous random variable.

Question 73

A small grocery store is considering installing an express checkout line. Let X be the number of customers in the regular checkout line. Note that these numbers include the customers being served, if any. The probability distribution of X is given in the table below.
Find the probability that one customer is in the regular checkout line.

Question 74

The number of car insurance policy holders is an example of a discrete random variable.

Question 75

What is the probability that this project will not be completed on time?

Question 76

The temperature of the room in which you are writing this test is a continuous random variable.

Question 77

The possible annual percentage return of the stocks of Gamma, Inc. and Delta, Inc. share a common probability distribution, given below.
(A) What is the expected annual return of each stock?
(B) What is the standard deviation of the annual return of each stock?
(C) On the basis of your answers to (A) and (B), which of these stocks would you prefer to buy? Defend your choice.
(D) Are the annual returns of these two stocks positively or negatively associated with each other? How might the answer to this question influence your decision to purchase shares?

Question 78

If a new pipeline will be constructed in the event that all three wells are successful, what is the probability that the pipeline will be constructed?

Question 79

A small grocery store is considering installing an express checkout line. Let X be the number of customers in the regular checkout line. Note that these numbers include the customers being served, if any. The probability distribution of X is given in the table below.
Find the probability that at least two people are in line.

Question 80

The number of people entering a shopping mall on a given day is an example of a discrete random variable.