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In probability theory, a probability space or a probability triple (Ω, F, P) {\displaystyle (\Omega,{\mathcal {F}},P)} is a mathematical construct that provides a formal model of a random process or "experiment". For example, one can define a probability space which models the throwing of a die.

A probability space consists of three elements:

In order to provide a model of probability, these elements must satisfy probability axioms.

In the example of the throw of a standard die,

When an experiment is conducted, it results in exactly one outcome ω {\displaystyle \omega } from the sample space Ω {\displaystyle \Omega }. All the events in the event space F {\displaystyle {\mathcal {F}}} that contain the selected outcome ω {\displaystyle \omega } are said to "have occurred". The probability function P {\displaystyle P} must be so defined that if the experiment were repeated arbitrarily many times, the number of occurrences of each event as a fraction of the total number of experiments, will most likely tend towards the probability assigned to that event.

The Soviet mathematician Andrey Kolmogorov introduced the notion of a probability space and the axioms of probability in the 1930s. In modern probability theory, there are alternative approaches for axiomatization, such as the algebra of random variables.