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In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]
Probability is the branch of mathematics and statistics concerning 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. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...
The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a particular ...
The probability measure is a set function returning an event's probability. A probability is a real number between zero (impossible events have probability zero, though probability-zero events are not necessarily impossible) and one (the event happens almost surely, with almost total certainty).
In probability theory, Kolmogorov's zero–one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, namely a tail event of independent σ-algebras, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one. Tail events are defined in ...
However, the probability of two events occurring together (that is, in conjunction) is always less than or equal to the probability of either one occurring itself—formally, for two events A and B this inequality could be written as () and () ().
With replacement, the probability would be 26/52 × 13/52 × 2 = 676/2704, or 13/52. In probability theory, the word or allows for the possibility of both events happening. The probability of one or both events occurring is denoted P(A ∪ B) and in general, it equals P(A) + P(B) – P(A ∩ B). [3]
This is called the addition law of probability, or the sum rule. That is, the probability that an event in A or B will happen is the sum of the probability of an event in A and the probability of an event in B, minus the probability of an event that is in both A and B. The proof of this is as follows: Firstly,