If A and B are any two events such that P(A) = 2/5 and P(A∩B) = 3/20, then the conditional probability, P(A|(A'∪B')), where A' denotes the complement of A, is equal to:

P(A) = 2/5 and P(A∩B) = 3/20, then
P(A|(A'∪B')) = P(A∩(A'∪B')) / P(A'∪B')
Since A∩(A'∪B') = (A∩A')∪(A∩B') = Ø∪(A∩B') = A∩B'
Therefore, P(A∩(A'∪B')) = P(A∩B') = P(A) - P(A∩B) = 2/5 - 3/20 = 8/20 - 3/20 = 5/20 = 1/4
P(A'∪B') = 1 - P(A∪B) = 1 - [P(A) + P(B) - P(A∩B)]
We don't have P(B), so we use another approach:
P(A|(A'∪B')) = P(A∩(A'∪B')) / P(A'∪B')
= P(A∩B') / P(A'∪B')
= [P(A) - P(A∩B)] / [1 - P(A∩B)]
= (2/5 - 3/20) / (1 - 3/20)
= (1/4) / (17/20)
= (1/4) * (20/17)
= 5/17