Probability

Definitions

Probability Experiment

Process which leads to well-defined results call outcomes

Outcome

The result of a single trial of a probability experiment

Sample Space

Set of all possible outcomes of a probability experiment

Event

One or more outcomes of a probability experiment

Classical Probability

Uses the sample space to determine the numerical probability that an event will happen. Also called theoretical probability.

Equally Likely Events

Events which have the same probability of occurring.

Complement of an Event

All the events in the sample space except the given events.

Empirical Probability

Uses a frequency distribution to determine the numerical probability. An empirical probability is a relative frequency.

Subjective Probability

Uses probability values based on an educated guess or estimate. It employs opinions and inexact information.

Mutually Exclusive Events

Two events which cannot happen at the same time.

Disjoint Events

Another name for mutually exclusive events.

Independent Events

Two events are independent if the occurrence of one does not affect the probability of the other occurring.

Dependent Events

Two events are dependent if the first event affects the outcome or occurrence of the second event in a way the probability is changed.

Conditional Probability

The probability of an event occurring given that another event has already occurred.

Bayes' Theorem

A formula which allows one to find the probability that an event occurred as the result of a particular previous event.

Factorial

A positive integer factorial is the product of each natural number up to and including the integer.

Permutation

An arrangement of objects in a specific order.

Combination

A selection of objects without regard to order.

Tree Diagram

A graphical device used to list all possibilities of a sequence of events in a systematic way.