Deck 5: Probability

Question 1

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

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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 3

True

Question 4

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 5

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

Question 6

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

Question 7

The probability of the intersection is called a joint probability.

Question 8

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

Question 9

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 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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 18

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

Question 19

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

Question 20

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

Question 21

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 22

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

Question 23

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

Question 24

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

Question 25

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

Question 26

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 27

Conditional probabilities are also called likelihood probabilities.

Question 28

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

Question 29

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

Question 30

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 31

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

Question 32

Events A and B are either independent or mutually exclusive.

Question 33

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

Question 34

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 35

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

Question 36

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

Question 37

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

Question 38

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

Question 39

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

Question 40

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

Question 41

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 42

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

A)P ( O_i )£ 0 for each i
B)P ( O_i )³ 1 for each i
C)0 £ P ( O_i )£ 1 for each i
D)P ( O_i )= 1 for each i

Question 43

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 44

Prior probability is also called likelihood probability.

Question 45

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 46

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

Question 47

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 48

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

Question 49

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 50

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 51

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

Question 52

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 53

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

Question 54

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 55

If an experiment consists of five outcomes with P ( O ₁)= 0.10, P ( O ₂)= 0.20, P ( O ₃)= 0.30, P ( O ₄)= 0.25, then P ( O ₅)is

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

Question 56

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 57

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

Question 58

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

Question 59

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 60

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

Question 61

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 62

The collection of all possible events is called

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

Question 63

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 64

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 65

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 66

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 67

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 68

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 69

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 70

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 71

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 72

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 73

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 74

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 75

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 76

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 77

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 78

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 ×.85)= .490

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

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