1Cademy - Conditional Probability

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Topics in Probability Theory

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Conditional Probability

Conditional probability is the likelihood of an event occurring, given that another event has already occurred. The event that is given must have a non-zero probability. This relationship is commonly denoted as $P(A|B)$ or $Pr(A|B)$ , which reads as 'the probability of A given B'. More generally, it can be represented as $Pr(\cdot|x_1, ..., x_n)$ or simply $p(\cdot|x_1, ..., x_n)$ , indicating the probability distribution of a variable conditioned on the values of other variables $x_1, ..., x_n$ .