If A and B are two events such that P (A) = 1/4 , P (B) = 1/2 and P (A ∩ B) = 1/8, find P (not A and not B).

Given: P (A) =, P (B) = and P (A ∩ B) =

P(not A and not B) = P(A^{’} ∩ B^{’})

As, { A^{’} ∩ B^{’} =(A ∪ B)^{’}}

⇒ P(not A and not B) = P ((A ∪ B)^{’})

= 1 - P (A ∪ B)

= 1- [P(A) + P(B) - P (A ∩ B)]

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