Events

Sample spaces#

The set of all possible outcomes of a random experiment is its sample space, written . For one roll of a die, .

An event is a subset of . "Roll an even number" is the event .

Operations on events#

Events combine like sets. In the figure, the overlap of the two circles is .

Axioms of probability#

Probability

A function assigns every event a number in such that

1. ;
2. for pairwise disjoint events , .

Inclusion–exclusion

For any events and ,

The subtracted term is exactly the overlap in the figure: and each counted it once.