# QBA Ch 5

computing the chance that something will occur in the future

statistical inference

deals with conclusion about a population based on a sample taken from that population

statistical inference

number that describes the chance that something will happen

Probability

a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur.

Probability

A process that leads to the occurrence of one and only one of several possible observations.

Experiment

A particular result of an experiment

Outcome

subdivided into (1) classical probability and (2) empirical probability.

Objective Probability

Objective Probability is subdivided into (1)_______________ probability and (2) empirical probability.

classical

Objective Probability is subdivided into (1) classical probability and (2) __________ probability.

empirical

a subdivision of objective probability which is based on the assumption that the outcomes of an experiment are equally likely.

Classical Probability

The occurrence of one event means that none of the other events can occur at the same time.

Mutually Exclusive

At least one of the events must occur when an experiment is conducted.

Collectively Exhaustive

second type of objective probability based on the number of times an event occurs as a proportion of a known number of trials.

Empirical frequency (relative frequency)

the probability of an event happening is the fraction of time similar events have happened in the past.

Empirical Probability

Over a large number of trials the empirical probability of an event will approach its true probability.

Law of Large Numbers

individual evaluates the available opinions and information and then estimates or assigns the probability.

Subjective Probability

the likelihood (probability) of a particular event happening that is assigned by an individual based on whatever information is available.

Subjective Concept of Probability

events must be mutually exclusive and then the probability of one event occurring equals the sum of their probabilities. P(A or B) = P(A) + P(B)

Special Rule of Addition

used to determine the probability of an event occurring by subtracting the probability of the event not occurring by 1.

Complement Rule

A probability that measures the likelihood two or more events will happen concurrently.

Joint Probability

events are not mutually exclusive and then the probability P(A or B) = P(A) + P(B) - P(A and B)

General Rule of Addition

For the expression P(A or B), the word "or" suggests that A may occur or B may occur. This also includes the possibility that A and B may occur.

inclusive

The occurrence of one event has no effect on the probability of the occurrence of another.

Independence

For two independent events A and B, the probability that A and B will both occur is found by multiplying the two probabilities. P(A and B) = P(A)P(B). Or for three independent events P(A and B and C) = P(A)P(B)P(C).

Special Rule of Multiplication

if two events are not independent

dependent

the probability of a particular event, given that another event has occurred.

Conditional Probability

used to find the joint probability of two events that are not independent; For two events, A and B, the joint probability that both event will happen is found by multiplying the probability that event A will happen by the conditional probability that event B occurring given that A has occurred.P(A and B) = P(A) P(B | A)

General Rule of Multiplication

A table used to classify sample observations according to two or more identifiable characteristics; a cross tabulation that simultaneously summarizes two variables of interest and their relationship.

Contingency Table

a graph that is helpful in organizing calculations that involve several stages. Each segment in the tree is one stage of the problem. The branches of a tree diagram are weighted by probabilities.

Tree Diagram

is applied to find the possible arrangements when there is more than one group of objects. It states If there are m ways of doing one thing and n ways of doing the other thing, there are (m * n) ways of doing both.

Multiplication Formula

is applied to find the possible arrangements when there is only one group of objects

Permutation Formula

Any arrangement of r objects selected from a single group of n possible objects and where n is the total number of objects and r is the number of objects selected.

Permutation

Any selection where the order of the selected objects are not important.

Combination