Deck 5: Probability

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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

Answer 3

False

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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 14

The probability of the intersection is called a joint probability.

Question 15

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 16

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

Question 17

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 18

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

Question 19

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

Question 20

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

Question 21

Assume that A and B are independent events with P(A) = 0.30 and P(B) = 0.50. The probability that both events will occur simultaneously is 0.80.

Question 22

Conditional probabilities are also called likelihood probabilities.

Question 23

The probability of the union of two mutually exclusive events A and B is 0.

Question 24

When A and B are mutually exclusive, P(A or B) can be found by adding P(A) and P(B).

Question 25

If P(B) = .7 and P(B|A) = .4, then P(A and B) must be .28.

Question 26

If A and B are two independent events with P(A) = 0.9 and P(B|A) = 0.5, then P(A and B) = 0.45.

Question 27

Posterior probability of an event is the revised probability of the event after new information is available.

Question 28

If the event of interest is A, the probability that A will not occur is the complement of A.

Question 29

Julius and Gabe go to a show during their Spring break and toss a balanced coin to see who will pay for the tickets. The probability that Gabe will pay three days in a row is 0.125.

Question 30

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

Question 31

Two events A and B are said to be mutually exclusive if P(A and B) = 1.0.

Question 32

If P(A and B) = 1, then A and B must be mutually exclusive.

Question 33

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

Question 34

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

Question 35

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 36

Prior probability of an event is the probability of the event before any information affecting it is given.

Question 37

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

Question 38

If P(B) = .7 and P(A|B) = .7, then P(A and B) = 0.

Question 39

Events A and B are either independent or mutually exclusive.

Question 40

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

Question 41

Prior probability is also called likelihood probability.

Question 42

We can apply the multiplication rule to compute the probability that two events occur at the same time.

Question 43

Suppose we have two events A and B. We can apply the addition rule to compute the probability that at least one of these events occurs.

Question 44

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 45

Posterior probabilities can be calculated using the addition rule for mutually exclusive events.

Question 46

In problems where the joint probabilities are given, we can compute marginal probabilities by adding across rows and down columns.

Question 47

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 48

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

Question 49

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.

Question 50

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 51

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 52

If joint, marginal, and conditional probabilities are available, only joint probabilities can be used to determine whether two events are dependent or independent.

Question 53

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 54

Prior probabilities can be calculated using the multiplication rule for mutually exclusive events.

Question 55

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 56

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 57

In general, a posterior probability is calculated by adding the prior and likelihood probabilities.

Question 58

We can use the joint and marginal probabilities to compute conditional probabilities, for which a formula is available.

Question 59

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 60

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 61

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 62

The probability of event A gives event B is denoted by

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

Question 63

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 64

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 65

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 66

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 67

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 68

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 -0 (.6 * .85) = .490

Question 69

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 70

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 71

The collection of all possible events is called

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

Question 72

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 73

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 74

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.

Question 75

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 76

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 77

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 78

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 79

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 80

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