Conditional probability

Probability of an event occurring, given that another event has already occurred

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred. This particular method relies on event A occurring with some sort of relationship with another event B. In this situation, the event A can be analyzed by a conditional probability with respect to B. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B) or occasionally PB(A). This can also be understood as the fraction of probability B that intersects with A, or the ratio of the probabilities of both events happening to the "given" one happening (how many times A occurs rather than not assuming B has occurred): .

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