Bayes' theorem

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How the probability of an event changes with new information? 

Let little dashes represent the probabilities of events A and B

A - - -

B     - - - - 

Only 1 dash is intersecting 

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P(B|A) = P(A & B) / P(B) = 1/4

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P(A|B) = P(A & B) / P(A)

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P(A|B) = P(B|A) P(B) / P(A)