Editing Probability (section)

{{short description|Branch of mathematics concerning chance and uncertainty}}
{{Distinguish|probability theory|game theory|graph theory|statistics}}
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[[File:Dice Distribution (bar).svg|thumb|250px|The probabilities of rolling several numbers using two dice]]

'''Probability''' is a branch of [[mathematics]] and [[statistics]] concerning [[Event (probability theory)|events]] and numerical descriptions of how likely they are to occur.  The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur.{{NoteTag|Strictly speaking, a probability of 0 indicates that an event [[almost surely|''almost'' never]] takes place, whereas a probability of 1 indicates than an event [[almost surely|''almost'' certainly]] takes place. This is an important distinction when the [[sample space]] is infinite. For example, for the [[continuous uniform distribution]] on the [[real number|real]] interval [5, 10], there are an infinite number of possible outcomes, and the probability of any given outcome being observed – for instance, exactly 7 – is 0. This means that an observation will ''almost surely not'' be exactly 7. However, it does '''not''' mean that exactly 7 is ''impossible''. Ultimately some specific outcome (with probability 0) will be observed, and one possibility for that specific outcome is exactly 7.}}<ref name="Stuart and Ord 2009">"Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), {{ISBN|978-0-534-24312-8}}.</ref><ref name="Feller">William Feller, ''An Introduction to Probability Theory and Its Applications'', vol.&nbsp;1, 3rd ed., (1968), Wiley, {{ISBN|0-471-25708-7}}.</ref> This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

These concepts have been given an [[Probability axioms|axiomatic]] mathematical formalization in ''[[probability theory]]'', which is used widely in [[areas of study]] such as [[statistics]], [[mathematics]], [[science]], [[finance]], [[gambling]], [[artificial intelligence]], [[machine learning]], [[computer science]], [[game theory]], and [[philosophy]] to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of [[complex systems]].<ref>[http://www.britannica.com/EBchecked/topic/477530/probability-theory Probability Theory]. The Britannica website.</ref>