# Probability

A number between 0 and 1 which represents how likely an event is to occur. Events with probability equal to 0 never occur. Events with probability equal to 1 always occur.

In data analysis, probability is normally defined in terms of the relative frequency of occurrence of an event which can be repeated many times. For example, if you repeatedly sample temperatures from a process and get values below 150 degrees half the time, then the "probability" of getting a reading below 150 degrees is equal to 0.5 or 50%.

In daily life, we sometimes use probability in a different sense, i.e., to express our degree of belief about the likelihood of an event which can not be repeated indefinitely under identical conditions. For example, you might say that the chance of getting a raise this year is "one in a million". Such "subjective" probabilities are sometimes used in statistical decision theory.

The three axioms of probability are:

- The probability of an event is a real number greater than or equal to zero;
- The sum of the probabilities of all possible outcomes of a given experiment is 1;
- If two events cannot both occur at the same time, the chance that either one occurs is the sum of the chances that each occurs.

**See also: **Bayes Rule, Complementary Probability, Conditional Probability, Cumulative Probability, Equally Likely, Event, Experimental Probability, Frequency View, Joint Probability, Multiplication Rule, Odds, Permutations and Combinations, Statistic, Theoretical Probability.

**Subjects: ** Statistics