Bayes' Theorem Definition

A theorem establishing a method of calculating conditional statistical probabilities, in which a known probability is modified in the light of later events that affect the data under consideration (Ex.: the probability of selecting a heart from a deck of cards is 13/52; if a card is selected from a full deck and that card is a heart, the probability that the next card selected will also be a heart becomes 12/51, but if that first selected card is not a heart, the probability for the next card becomes 13/51)

A theorem which states that an already-known unconditioned probability (the "prior") of some target event can be multiplied by a "likelihood ratio" — the conditional probability of a certain factor event (given the pri) divided by the marginal probability of that factor — in order to obtain the ("posterior", i.e., the) conditional probability of the target given the factor.