# Probability

According to English Wikipedia:

In science, the probability of an event 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 is 0; that of an event that is certain to occur is 1. 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%).

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 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).

1. Copied and adapted intro text from English Wikipedia (w:Probability; https://en.wikipedia.org/w/index.php?title=Probability&oldid=1139278145 )
2. w:Event (probability theory)
3. w:impossible event
4. 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.
5. "Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), ISBN: 978-0-534-24312-8.
6. William Feller, An Introduction to Probability Theory and Its Applications, (Vol 1), 3rd Ed, (1968), Wiley, ISBN: 0-471-25708-7.