# A Survey of Probability Concepts

Classical Probability

based on the assumption that the outcomes of an experiment are equally likely.

Classical Probability (Formula)

P(E)= # of favorable outcomes/Total # of possible outcomes

Mutually Exclusive

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

Events must be mutually exclusive:P(A OR B) = P(A) + P(B)For three mutually exclusive events designated A, B, and C, the rule is written:P(A or B or C) = P(A) + P(B) + P(C)

Complement Rule

The probability of an event occurring is 1 minus the probability that it doesn't occur. P(A) = 1 - P(~A)

Collectively Exhaustive

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

Empirical Probability

Probability based on actual experience or historical data.

Empirical Probability (Formula)

Empirical Probability = # of times the event occurs/Total # of observations

Law of Large Numbers

As the sample size gets larger, each sample average is more likely to be closer to the population average.

Subjective Concept of Probability

The likelihood of a particular event happening that is assigned by an individual based on whatever information is available.

Joint Probability

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

P(A or B) = P(A) + (B) - (A and B)

Independence

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

Special Rule of Multiplication

P(A and B) = P(A)P(B)

Conditional Probability

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

General Rule of Multiplication

P(A and B) = P(A)P(B|A)

Contingency Table

A table used to classify sample observations according to two or more identifiable characteristics

Prior Probability

The initial probability based on the present level of information

Posterior Probability

A revised probability based on additional information

Multiplication Formula

If there are m ways of doing one thing and n ways of doing another thing, there are m x n ways of doing both.

Multiplication Formula (Formula)

Total number of arrangements = (m)(n)

Permutation

Any arrangement of r objects selected from a single group of n possible objects.

Permutation Formula

nPr = n! / (n-r)!

Combination Formula

nCr = n!/r!(n-r)!