If A and B are events at the same experiments with P(A) = 0.2, P(B) = 0.5, then maximum value of P(A' ∩ B) is:

1/2

P(A' ∩ B) = P(A') - P(B) - P(A' ∪ B) = 0.8 - 0.5 - P(A' ∪ B)

P(A' ∩ B) is max when P(A' ∪ B) is minimum

But as P(A' ∪ B) = max{P(A'), P(B')} = 0.8 (in the case when smaller set is a subset of larger)

⇒ P(A' ∩ B) = 0.5