STAT 351 Chapter #6

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

False

In applying Bayes' Law, as the prior probabilities increase, the posterior probabilities decrease.

False

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

False

If event A and event B cannot occur at the same time, then A and B are said to be a. mutually exclusive c. collectively exhaustive b. independent d. None of these choices.

A

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.

A

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.

A

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.

B

The collection of all possible outcomes of an experiment is called: a. a simple event c. a sample b. a sample space d. a population

B

Which of the following is an approach to assigning probabilities? a. Classical approach c. Subjective approach b. Relative frequency approach d. All of these choices are true.

B

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 c. 3 b. At most 2 d. 15

C

An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the: a. subjective approach c. classical approach b. objective approach d. relative frequency approach

C

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.

D

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.

D

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

False

Bayes' Law says that P(A|B) = P(B|A)P(A).

False

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

P(A)

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

Sum

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

T

Although there is a formula defining Bayes' law, you can also use a probability tree to conduct calculations.

True

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

True

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

True

If A and B are mutually exclusive, their joint probability is ____________________.

Zero;0

If two events are mutually exclusive, their joint probability is ____________________.

Zero;0

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.

a. Subjective b. Classical c. relative frequency

The ____________________ rule is used to calculate the probability of the union of two events.

addition

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.

b

The collection of all possible events is called a. an outcome c. an event b. a sample space d. None of these choices.

b

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.

c

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.

d

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

relative frequency approach

If two events are mutually exclusive their joint probability is ____________________.

zero; 0

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

False

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

False

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

False

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

True

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

True

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 c. 0.50 b. 0.90 d. None of these choices.

A

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

False

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. c. cannot be larger than 0.25. b. can be any value between 0 and 0.75. d. equals 0.25.

C

If you roll a balanced die 50 times, you should expect an even number to appear: a. on every other roll. c. 25 times on average, over the long term. b. exactly 50 times out of 100 rolls. d. All of these choices are true.

C

Which of the following is a requirement of the probabilities assigned to outcome Oi? a. P(Oi) £ 0 for each i c. 0 £ P(Oi) £ 1 for each i b. P(Oi) ³ 1 for each i d. P(Oi) = 1 for each i

C

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.

False

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

False

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

False

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

False

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.

True

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

True

The probability of the intersection is called a joint probability.

True

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'.

True

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.

d

P(A|B) is the conditional probability of ____________________ given ____________________.

A;B

The ____________________ rule says that P(Ac) = 1 - P(A).

Complement

The second set of branches of a probability tree represent ____________________ probabilities.

Conditional

If A and B are ____________________ events, the joint probability of A and B is the product of the probabilities of those two events.

Independent

If P(A|B) = P(A) then events A and B are ____________________.

Independent

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

Intersection

A posterior probability value is a prior probability value that has been: a. modified on the basis of new information. b. multiplied by a conditional probability value. c. divided by a conditional probability value. d. added to a conditional probability value.

A

If events A and B are independent then: a. P(A and B) = P(A) * P(B) b. P(A and B) = P(A) + P(B) c. P(B|A) = P(A) d. None of these choices.

A

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.

A

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

A

Which of the following statements is false regarding a scenario using Bayes' Law? a. Prior probabilities are called likelihood probabilities. b. Conditional probabilities are called posterior probabilities. c. Posterior probabilities are calculated by using prior probabilities that have been modified based on new information. d. None of these choices.

A

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

True

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.

True

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

True

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

True

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.

True

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

True

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

True

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

True

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

True

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

True

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

Two ; 2

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

Union

Bayes' Law involves three different types of probabilities: 1) prior probabilities; 2) ____________________ probabilities; and 3) posterior probabilities.

likelihood

In the scenario of Bayes' Law, P(A|B) is a posterior probability, while P(B|A) is a(n) ____________________ probability.

likelihood

In the scenario of Bayes' Law, P(A|B) is a(n) ____________________ probability, while P(B|A) is a posterior probability.

likelihood

The ____________________ rule is used to calculate the joint probability of two events.

multiplication

If two events are complements, their probabilities sum to ____________________.

one; 1

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

outcomes

Bayes' Law involves three different types of probabilities: 1) prior probabilities; 2) likelihood probabilities; and 3) ____________________ probabilities.

posterior

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

simple

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

False

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

False

Prior probability is also called likelihood probability.

False

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

False

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

True

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.

B

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

B

Which of the following statements is false? a. Thomas Bayes first employed the calculation of conditional probability in the eighteenth century. b. There is no formula defining Bayes' Law. c. We use a probability tree to conduct all necessary calculations for Bayes' Law. d. None of these choices.

B

Thomas ____________________ first employed the calculation of conditional probability.

Bayes

There are situations where we witness a particular event and we need to compute the probability of one of its possible causes. ____________________ is the technique we use to do this.

Bayes Law

____________________ can find the probability that someone with a disease tests positive by using (among other things) the probability that someone who actually has the disease tests positive for it.

Bayes Law

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

C

If P(A) = 0.20, P(B) = 0.30, and P(A and B) = 0, then A and B are: a. dependent events b. independent events c. mutually exclusive events d. complementary events

C

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.

C

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)

C

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.

C

Initial estimates of the probabilities of events are known as: a. joint probabilities b. posterior probabilities c. prior probabilities d. conditional probabilities

C.

Which of the following statements is always correct? a. P(A and B) = P(A) * P(B) b. P(A or B) = P(A) + P(B) c. P(A) = 1 - P(Ac) d. None of these choices.

C.

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

D

Two events A and B are said to be mutually exclusive if: a. P(A|B) = 1 b. P(A|B) = P(A) c. P(A and B) =1 d. P(A and B) = 0

D

Bayes' Law is used to compute: a. prior probabilities. b. joint probabilities. c. union probabilities. d. posterior probabilities.

D.

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.

False

Bayes' Law can be used to calculate posterior probabilities, prior probabilities, as well as new conditional probabilities.

False

Events A and B are either independent or mutually exclusive.

False

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

False

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

False

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

False

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

False

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

False

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

False

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

False

The probability of an intersection of two events is called a(n) ____________________ probability.

Joint

When you multiply a first level branch with a second level branch on a probability tree you get a(n) ____________________ probability.

Joint

Suppose two events A and B are related. The ____________________ probability of A is the probability that A occurs, regardless of whether event B occurred or not.

Marginal

The first set of branches of a probability tree represent ____________________ probabilities.

Marginal

If A and B are ____________________ then the probability of the union of A and B is the sum of their individual probabilities

Mutually Exclusive

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

Mutually Exclusive

A conditional probability of A given B is written in probability notation as ____________________.

P(A|B)

Bayes' Law involves three different types of probabilities: 1) ____________________ probabilities; 2) likelihood probabilities; and 3) posterior probabilities.

Prior

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.

Relative frequency

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

Sample space

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.

T

Bayes' Law allows us to compute conditional probabilities from other forms of probability.

True

Bayes' Law is a formula for revising an initial subjective (prior) probability value on the basis of new results, thus obtaining a new (posterior) probability value.

True

Conditional probabilities are also called likelihood probabilities.

True

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.

True

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

True

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

True

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

event

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

exhaustive

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

exhaustive; mutually exclusive mutually exclusive; exhaustive