Monday, February 7, 2011

Conditional probability

Conditional probability: The conditional probability of an event A assuming that B has occurred, denoted P(A|B), equals P(A|B) = (P(A intersection B))/(P(B)), which can be proven directly using a Venn diagram. Multiplying through, this becomes P(A|B)P(B) = P(A intersection B), which can be generalized to P(A intersection B intersection C) = P(A)P(B|A)P(C|A intersection B). 
Rearranging (-3) gives P(B|A) = (P(B intersection A))/(P(A)).

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