Let E c denotes the complement of an event E . Let E , F , G be pairwise independent events with P ( G ) 0 and P ( E ∩ F ∩ G ) = 0 . Then, P ( E c ∩ F c ∣ G ) equals

Question

Let E c denotes the complement of an event E . Let E , F , G be pairwise independent events with P ( G ) > 0 and P ( E ∩ F ∩ G ) = 0 . Then, P ( E c ∩ F c ∣ G ) equals

TestHub · Accepted Answer

P ( G E c ∩ F c ​ ) ​ = P ( G ) P ( E c ∩ F c ∩ G ) ​ = P ( G ) P ( G ) − P ( E ∩ G ) − P ( G ∩ F ) ​ = P ( G ) P ( G ) [ 1 − P ( E ) − P ( F )] ​ = 1 − P ( E ) − P ( F ) = P ( E c ) − P ( F ) . ​

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