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Probability: Difference between revisions
added Category:Mathematics Category:Probability Category:Glossary
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According to English Wikipedia:<ref>Copied and adapted intro text from English Wikipedia ([[w:Probability]]; https://en.wikipedia.org/w/index.php?title=Probability&oldid=1139278145 )</ref>
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[[File:Dice Distribution (bar).svg|thumb|250px|The probabilities of rolling several numbers using two dice.]]
In [[science]], the '''probability''' of an event<ref>[[w:Event (probability theory)]]</ref> is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability. The probability of an impossible event<ref>[[w:impossible event]]</ref> is 0; that of an event that is certain to occur is 1.<ref>The converse is not necessarily true. Strictly speaking, a probability of 0 indicates that an event ''almost'' never takes place, whereas a probability of 1 indicates than an event ''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 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 when we make an observation, it 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><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 1), 3rd Ed, (1968), Wiley, {{ISBN|0-471-25708-7}}.</ref> The probabilities of two complementary events ''A'' and ''B'' – either ''A'' occurs or ''B'' occurs – add up to 1. A simple example is the tossing of a fair (unbiased) coin. If a coin is fair, the two possible outcomes ("heads" and "tails") are equally likely; since these two outcomes are complementary and the probability of "heads" equals the probability of "tails", the probability of each of the two outcomes equals 1/2 (which could also be written as 0.5 or 50%).
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Probability sometimes appears in the context of voting theory when discussing who should win an election. When there is a tie, multiple candidates may have a positive probability of winning.
As a result, some voting method criteria are/must be defined with respect to candidates having or not having positive probabilities of winning, rather than winning or not winning. For example, the [[Plurality criterion|plurality criterion]] can be defined either as "B must not win" or "A's probability of winning must be at least as good as B's" (see also [[W:Plurality criterion]]).
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[[Category:Mathematics]]
[[Category:Probability]]
[[Category:Glossary]]
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