If two events A and B are such that P(A′) = 0.3, P(B) = 0.4 and P(AB′) = 0.5, then
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P(A) = 1 − P(A′) = 1 − 0.3 = 0.7, P(B) = 0.4
We know that
P(A) = P(A∩B) + P(A∩B′) ⇒ 0.7 = P(A∩B) = 0.5
⇒ P(A∩B) = 0.7 − 0.5 = 0.2
P(A⋃B′) = P(A) + P(B′) − P(A∩B′) = 0.7 + (1 − 0.4) − 0.5 = 0.8
Next
From set theory B∩(A∩B′) = (B∩A)⋃(B∩B′) = (B∩A) ⋃ ϕ = B∩A
∴ Required probability
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