Verified answer

P(A∩B) = P(A) + P(B) - P(A∪B) [this is always true]

= 0.65 + 0.45 - 0.9

= 0.2.

Also P(A∩B') must satisfy P(A∩B) + P(A∩B') = P(A), so P(A∩B') = P(A) - P(A∩B)

= 0.65 - 0.2

= 0.45

Similarly P(A'∩B) must satisfy P(A∩B) + P(A'∩B) = P(B), so P(A'∩B) = P(B) - P(A∩B)

= 0.45 - 0.2

= 0.25.