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).

Question

Philoid · Accepted Answer

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)]