Deck 6: Probability

Question 1

An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the:

A) subjective approach
B) objective approach
C) classical approach
D) relative frequency approach

Answer 1

classical approach

Question 2

If A and B are mutually exclusive events with P(A) = 0.75, then P(B):

A) can be any value between 0 and 1.
B) can be any value between 0 and 0.75.
C) cannot be larger than 0.25.
D) equals 0.25.

Answer 2

cannot be larger than 0.25.

Question 3

P(A) + P(B) = 1 for any events A and B that are mutually exclusive.

Answer 3

False

Question 4

Of the last 500 customers entering a supermarket, 50 have purchased a wireless phone.If the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is

A) 0.10
B) 0.90
C) 0.50
D) None of these choices.

Question 5

If events A and B cannot occur at the same time, they are called mutually exclusive.

Question 6

You think you have a 90% chance of passing your next advanced financial accounting exam.This is an example of subjective approach to probability.

Question 7

Predicting the outcome of a football game is using the subjective approach to probability.

Question 8

If an experiment consists of five outcomes with P(O₁) = 0.10, P(O₂) = 0.20, P(O₃) = 0.30, P(O₄) = 0.25, then P(O₅) is

A) 0.75
B) 0.15
C) 0.50
D) Cannot be determined from the information given.

Question 9

If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive.

Question 10

If you roll a balanced die 50 times, you should expect an even number to appear:

A) on every other roll.
B) exactly 50 times out of 100 rolls.
C) 25 times on average, over the long term.
D) All of these choices are true.

Question 11

If either event A or event B must occur, then A and B are mutually exclusive and collectively exhaustive events.

Question 12

A sample space of an experiment consists of the following outcomes: 1, 2, 3, 4, and 5.Which of the following is a simple event?

A) At least 3
B) At most 2
C) 3
D) 15

Question 13

If two events are collectively exhaustive, what is the probability that one or the other occurs?

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

Question 14

Which of the following is a requirement of the probabilities assigned to outcome O_i?

A) P(O_i) $\le$ 0 for each i
B) P(O_i) $\ge$ 1 for each i
C) 0 $\le$ P(O_i) $\le$ 1 for each i
D) P(O_i) = 1 for each i

Question 15

The collection of all the possible outcomes of a random experiment is called a sample space.

Question 16

Which of the following is an approach to assigning probabilities?

A) Classical approach
B) Relative frequency approach
C) Subjective approach
D) All of these choices are true.

Question 17

The collection of all possible outcomes of an experiment is called:

A) a simple event
B) a sample space
C) a sample
D) a population

Question 18

The relative frequency approach to probability uses long term relative frequencies, often based on past data.

Question 19

If either event A or event B must occur, they are called mutually exclusive.

Question 20

If P(A) = 0.4 and P(B) = 0.6, then A and B must be mutually exclusive.

Question 21

The outcomes of a sample space must be ____________________, which means that all possible outcomes must be included.

Question 22

If event A and event B cannot occur at the same time, then A and B are said to be

A) mutually exclusive
B) independent
C) collectively exhaustive
D) None of these choices.

Question 23

A(n) ____________________ of a random experiment is a list of all possible outcomes of the experiment.

Question 24

No matter which approach was used to assign probability (classical, relative frequency, or subjective) the one that is always used to interpret a probability is the ____________________ approach.

Question 25

Alana, Eva, and Stephanie, three candidates for the presidency of a college's student body, are to address a student forum.The forum's organizer is to select the order in which the candidates will give their speeches, and must do so in such a way that each possible order is equally likely to be selected.
a.
What is the random experiment?
b.
List the outcomes in the sample space.
c.
Assign probabilities to the outcomes.
d.
What is the probability that Stephanie will speak first?
e.
What is the probability that Alana will speak before Stephanie does?

Question 26

The outcomes of a sample space must be ____________________ and ____________________.

Question 27

The outcomes of a sample space must be ____________________, which means that no two outcomes can occur at the same time.

Question 28

If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?

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

Question 29

A random experiment is an action or process that leads to one of several possible ____________________.

Question 30

The probability of an event is the ____________________ of the probabilities of the simple events that constitute the event.

Question 31

The collection of all possible events is called

A) an outcome
B) a sample space
C) an event
D) None of these choices.

Question 32

If two events are mutually exclusive, what is the probability that one or the other occurs?

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

Question 33

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) Cannot be determined from the information given.

Question 34

An individual outcome of a sample space is called a(n) ____________________ event.

Question 35

If events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?

A) 0.25
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 36

If the two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs?

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

Question 37

If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur?

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

Question 38

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) Cannot be determined from the information given.

Question 39

There are ____________________ requirements of probabilities for the outcomes of a sample space.

Question 40

A(n) ____________________ is a collection or set of one or more simple events in a sample space.

Question 41

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.

{Hobby Shop Sales Narrative} What is the probability of selling between 1 and 3 (inclusive) trucks in any given week?

Question 42

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan, based on past records.

{Equity Loan Rates Narrative} If a bank is selected at random from this distribution, what is the probability that the interest rate charged on a home loan exceeds 7.0%?

Question 43

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan, based on past records.

{Equity Loan Rates Narrative} What is the most common interest rate?

Question 44

The probability of the intersection is called a joint probability.

Question 45

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.

{Hobby Shop Sales Narrative} Define the random experiment of interest to the store.

Question 46

If A and B are independent events with P(A) = .40 and P(B) = .50, then P(A and B) = .20.

Question 47

Two or more events are said to be independent when the occurrence of one event has no effect on the probability that another will occur.

Question 48

Mutual Fund Price
An investor estimates that there is a 75% chance that a particular mutual fund's price will increase to $100 per share over the next three weeks, based on past data.
{Mutual Fund Price Narrative} Interpret the 75% probability.

Question 49

Equity Loan Rates
A survey of banks estimated the following probabilities for the interest rate being charged on a equity loan based on a 30-year loan, based on past records.

{Equity Loan Rates Narrative} What approach was used in estimating the probabilities for the interest rates?

Question 50

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.

{Hobby Shop Sales Narrative} What approach would you use in determining the probabilities for next week's sales? Assign probabilities to the outcomes.

Question 51

The sample space of the toss of a balanced die is S = {1, 2, 3, 4, 5, 6}.If the die is balanced, each simple event (outcome) has the same probability.Find the probability of the following events:
a.
Rolling an odd number
b.
Rolling a number less than or equal to 3
c.
Rolling a number greater than or equal to 5
d.
Rolling a number between 2 and 5, inclusive.

Question 52

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.

{Hobby Shop Sales Narrative} List the outcomes in the sample space.

Question 53

If A and B are independent events with P(A) = 0.35 and P(B) = 0.55, then P(A|B) is 0.35/0.55 = .64.

Question 54

Hobby Shop Sales
Sales records of a hobby shop showed the following number of radio controlled trucks sold weekly for each of the last 50 weeks.

{Hobby Shop Sales Narrative} What is the probability of selling at least two trucks in any given week?

Question 55

There are three approaches to determining the probability that an outcome will occur: classical, relative frequency, and subjective.For each situation that follows, determine which approach is most appropriate.
a.
A Russian will win the French Open Tennis Tournament next year.
b.
The probability of getting any single number on a balanced die is 1/6.
c.
Based on the past, it's reasonable to assume the average book sales for a certain textbook is 6,500 copies per month.

Question 56

The intersection of two events A and B is the event that occurs when both A and B occur.

Question 57

The union of events A and B is the event that occurs when either A or B or both occur.It is denoted as 'A or B'.

Question 58

Two events A and B are said to be independent if P(A|B) = P(B).

Question 59

Mutual Fund Price
An investor estimates that there is a 75% chance that a particular mutual fund's price will increase to $100 per share over the next three weeks, based on past data.
{Mutual Fund Price Narrative} Which approach was used to produce this figure?

Question 60

The conditional probability of event B given event A is denoted by P(A|B).

Question 61

A and B are disjoint events, with P(A) = 0.20 and P(B) = 0.30.Then P(A and B) is:

A) 0.50
B) 0.10
C) 0.00
D) 0.06

Question 62

If P(A) = 0.65, P(B) = 0.58, and P(A and B) = 0.76, then P(A or B) is:

A) 1.23
B) 0.47
C) 0.18
D) 0.11

Question 63

If A and B are independent, then P(A|B) = P(A) or P(B|A) = P(B).

Question 64

If P(A) = .30, P(B) = .60, and P(A and B) = .20, then P(A|B) = .40.

Question 65

If A and B are independent events with P(A) = 0.20 and P(B) = 0.60, then P(A|B) is:

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

Question 66

The probability of event A given event B is denoted by

A) P(A and B)
B) P(A or B)
C) P(A|B)
D) P(B|A)

Question 67

If A and B are independent events with P(A) = 0.60 and P(A|B) = 0.60, then P(B) is:

A) 1.20
B) 0.60
C) 0.36
D) cannot be determined with the information given

Question 68

Suppose the probability that a person owns both a cat and a dog is 0.10.Also suppose the probability that a person owns a cat but not a dog is 0.20.The marginal probability that someone owns a cat is 0.30.

Question 69

If the outcome of event A is not affected by event B, then events A and B are said to be

A) mutually exclusive
B) independent
C) collectively exhaustive
D) None of these choices.

Question 70

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

A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given

Question 71

The union of events A and B is the event that occurs when either A or B occurs but not both.

Question 72

If P(A) = 0.35, P(B) = 0.45, and P(A and B) = 0.25, then P(A|B) is:

A) 1.4
B) 1.8
C) 0.714
D) 0.556

Question 73

Which of the following statements is correct if the events A and B have nonzero probabilities?

A) A and B cannot be both independent and disjoint
B) A and B can be both independent and disjoint
C) A and B are always independent
D) A and B are always disjoint

Question 74

Suppose P(A) = 0.60, P(B) = 0.85, and A and B are independent.The probability of the complement of the event (A and B) is:

A) .4 * .15 = .060
B) 0.40 + .15 = .55
C) 1 -(.40 + .15) = .45
D) 1- (.6 *10 .85) = .490

Question 75

The probability of the intersection of two events A and B is denoted by P(A and B) and is called the:

A) marginal probability
B) joint probability
C) conditional probability of A given B
D) conditional probability of B given A

Question 76

Which of the following best describes the concept of marginal probability?

A) It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs.
B) It is a measure of the likelihood that a particular event will occur, if 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.

Question 77

If A and B are disjoint 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) cannot be determined with the information given

Question 78

Two events A and B are independent if P(A and B) = 0.

Question 79

The intersection of events A and B is the event that occurs when:

A) either A or B occurs but not both
B) neither A nor B occur
C) both A and B occur
D) All of these choices are true.

Question 80

Which of the following is equivalent to P(A|B)?

A) P(A and B)
B) P(B|A)
C) P(A)/P(B)
D) None of these choices.