Chapter 4

Question 1

Addition Law

Answer 1

A probability law used to compute the probability of the union of two events. It is P(A ∩ B) = P(A) + P(B) − P(A ∪ B). For mutually exclusive events, P(A ∩ B) = 0; in this case the addition law reduces to P(A ∪ B) = P(A) + P(B).

Question 1

Basic requirements for assigning probabilities

Answer 1

Two requirements that restrict the manner in which probability assignments can be made: (1) for each experimental outcome E; we must have 0 < P(E;) < 1; (2) considering all experimental outcomes, we must have
P(El) + P(Ez) +
.+P(E,)卡1.0

Question 2

Bayes’ Theorom

Answer 2

A method used to compute posterior probabilities.

Question 3

Classical Method

Answer 3

A method of assigning probabilities that is appropriate when all the experimental outcomes are equally likely.

Question 4

Combination

Answer 4

In an experiment we may be interested in determining the number of ways n objects may be selected from among N objects without regard to the order in which the n objects are selected. Each selection of n objects is called a combination and the total number of combinations of N objects taken n at a time is

Question 5

Complement of A

Answer 5

The event consisting of all sample points that are not in A.

Question 6

Conditional Probability

Answer 6

The probability of an event given that another event already occurred. The conditional probability of A given B is
P(A B) =
P(AMB)
P(B)

Question 7

Event

Answer 7

A collection of sample points.

Question 8

Experiment

Answer 8

A process that generates well-defined outcomes.

Question 9

Independant Events

Answer 9

Two events A and B where P(A | B) = P(A) or P(B | A) = P(B); that is, the events have no influence on each other.

Question 10

Intersection of A and B

Answer 10

The event containing the sample points belonging to both A and B. The intersection is denoted A ∩ B.

Question 11

Joint Probability

Answer 11

The probability of two events both occurring; that is, the probability of the intersection of two events.

Question 12

Marginal Probability

Answer 12

The values in the margins of a joint probability table that provide the probabilities of each event separately.

Question 13

Multiple-Step Experiment

Answer 13

An experiment that can be described as a sequence of steps.
If a multiple-step experiment has k steps with n1 possible outcomes on the first step, n2 possible outcomes on the second step, and so on, the total number of experimental outcomes is given by (nI) (12)… (nk).

Question 14

Multiplication Law

Answer 14

A probability law used to compute the probability of the intersection of two events. It is P(A ∩ B) = P(B)P(A | B) or P(A ∩ B) = P(A)P(B | A). For independent events it reduces to P(A ∩ B) = P(A)P(B).

Question 15

Mutually Exclusive Events

Answer 15

Events that have no sample points in common; that is, A ∩ B is empty and P(A ∩ B) = 0.

Question 16

Permutation

Answer 16

In an experiment we may be interested in determining the number of ways n objects may be selected from among N objects when the order in which the n objects are selected is important. Each ordering of n objects is called a permutation and the total number of permutations of N objects taken n at a time is for n = 0, 1, 2, …, N.

Question 17

Posterior Probabilities

Answer 17

Revised probabilities of events based on additional information.

Question 18

Prior Probabilities

Answer 18

Initial estimates of the probabilities of events.

Question 19

Probability

Answer 19

A numerical measure of the likelihood that an event will occur.

Question 20

Relative Frequency Method

Answer 20

A method of assigning probabilities that is appropriate when data are available to estimate the proportion of the time the experimental outcome will occur if the experiment is repeated a large number of times.

Question 21

Sample Point

Answer 21

An element of the sample space. A sample point represents an experimental outcome.

Question 22

Sample Space

Answer 22

The set of all experimental outcomes.

Question 23

Subjective Method

Answer 23

A method of assigning probabilities on the basis of judgment.

Question 24

Tree Diagram

Answer 24

A graphical representation that helps in visualizing a multiple-step experiment.

Question 25

Union of A and B

Answer 25

The event containing all sample points belonging to A or B or both. The union is denoted A ∪ B.

Question 26

Venn Diagram

Answer 26

A graphical representation for showing symbolically the sample space and operations involving events in which the sample space is represented by a rectangle and events are represented as circles within the sample space.