**Probability theory** is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted. Two representative mathematical results describing such patterns 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 large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.

Read more about Probability Theory: History, Treatment, Probability Distributions, Convergence of Random Variables, Law of Large Numbers, Central Limit Theorem

### Famous quotes containing the words probability and/or theory:

“Legends of prediction are common throughout the whole Household of Man. Gods speak, spirits speak, computers speak. Oracular ambiguity or statistical *probability* provides loopholes, and discrepancies are expunged by Faith.”

—Ursula K. Le Guin (b. 1929)

“[Anarchism] is the philosophy of the sovereignty of the individual. It is the *theory* of social harmony. It is the great, surging, living truth that is reconstructing the world, and that will usher in the Dawn.”

—Emma Goldman (1869–1940)