Editing Probability theory (section)

{{Short description|Branch of mathematics concerning probability}}
{{Probability fundamentals}}

'''Probability theory''' or '''probability calculus''' is the branch of [[mathematics]] concerned with [[probability]]. Although there are several different [[probability interpretations]], probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of [[axioms of probability|axioms]]. Typically these axioms formalise probability in terms of a [[probability space]], which assigns a [[measure (mathematics)|measure]] taking values between 0 and 1, termed the [[probability measure]], to a set of outcomes called the [[sample space]]. Any specified subset of the sample space is called an [[event (probability theory)|event]].

Central subjects in probability theory include discrete and continuous [[random variable]]s, [[probability distributions]], and [[stochastic process]]es (which provide mathematical abstractions of [[determinism|non-deterministic]] or uncertain processes or measured [[Quantity|quantities]] that may either be single occurrences or evolve over time in a random fashion).
Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability theory describing such behaviour are the [[law of large numbers]] and the [[central limit theorem]].

As a mathematical foundation for [[statistics]], probability theory is essential to many human activities that involve quantitative analysis of data.<ref>[http://home.ubalt.edu/ntsbarsh/stat-data/Topics.htm Inferring From Data]</ref> Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in [[statistical mechanics]] or [[sequential estimation]]. A great discovery of twentieth-century [[physics]] was the probabilistic nature of physical phenomena at atomic scales, described in [[quantum mechanics]].<ref>{{cite encyclopedia |title=Quantum Logic and Probability Theory |encyclopedia=The Stanford Encyclopedia of Philosophy |date=10 August 2021|url= https://plato.stanford.edu/entries/qt-quantlog/ }}</ref>