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Sample space (Ω)

Set of all possible outcomes of a random experiment.

Event

A subset of the sample space Ω.

Elementary (or atomic) event

An element of the sample space Ω viewed as event.

Mutually exclusive events

Two events that are disjoint as sets (i.e. their intersection is empty).

Power set

The set ℘(A) of all subsets of a given set A.

Additive function

A function P : ℘(Ω) → R satisfying P(A∪B) = P(A) + P(B) for all disjoint A, B ⊂ Ω.

Probability distribution (finite)

An additive function P from the powerset ℘(Ω) of a finite set Ω to [0,1] such that P(Ω) equals 1.

Countable set

A set with the same cardinality (number of elements) as some subset of the set of natural numbers.

Probability mass function (PMF)

A function P : Ω → [0,1] for a countable Ω such that the sum of the P(ω) over all ω in Ω equals 1.

Discrete probability space

A pair (Ω,P) of a non-empty countable sample space Ω and a probability distribution or mass function P.