The conditional probability of the event A given that the event B has occurred is described by Bayes Theorem (first developed by the English Reverend Thomas Bayes):

Pr (A \ B) = The probability of A, given that B has occurred:

Pr (B \ A) * Pr (A)
Pr (B \ A) * Pr (A) + Pr (B \ not A) * Pr (not A)


To illustrate the idea, this example is taken from 'IntroSTAT' by Les Underhill and Dave Bradfield:

You feel ill at night and stumble into the bathroom, grab one of three bottles in the dark and take a pill. An hour later you feel really ghastly, and you remember…

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