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Bayes’ formula makes use of the total probability rule. To review, that rule expressed the probability of an event as a weighted average of the probabilities of the event, given a set of scenarios. Bayes’ formula works in reverse; more precisely, it reverses the “given that” information. Bayes’ formula uses the occurrence of the event to infer the probability of the scenario generating it. For that reason, Bayes’ formula is sometimes called an inverse probability. In many applications, including the one illustrating its use in this section, an individual is updating his beliefs concerning the causes that may have produced a new observation.

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