Probability: Difference between revisions

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.{{NoteTag|note=The converse is not necessarily true. 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 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 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%).