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A probability space, in probability theory, is the conventional mathematical model of randomness. This mathematical object, sometimes called also probability triple, formalizes three interrelated ideas by three mathematical notions. First, a sample point (called also elementary event), --- something to be chosen at random (outcome of experiment, state of nature, possibility etc.) Second, an event, --- something that will occur or not, depending on the chosen elementary event. Third, the probability of an event. The definition (see below) was introduced by Kolmogorov in the 1930s. For an algebraic alternative to Kolmogorov's approach, see algebra of random variables. Alternative models of randomness (finitely additive probability, non-additive probability) are sometimes advocated in connection to various probability interpretations.

A probability space is a measure space such that the measure of the whole space is equal to 1.

In other words a probability space is a triple consisting of a set (called the sample space), a s-algebra (also called s-field) of subsets of (these subsets are called events), and a measure on such that (called the probability measure).

Discrete probability theory needs only at most countable sample spaces , which makes the foundations much less technical. Probabilities can be ascribed to points of by a function such that . All subsets of can be treated as events (thus, is the power set). The probability measure takes the simple form

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