Question

If A and B are events such that P(A ∪ B) = 0.5, P B( ) = 0.8 and P(A/B) = 0.4, then what is P(A ∩ B) equal to ? (a) 0.08 (b) 0.02 (c) 0.2 (d) 0.8 Select the correct answer from above options

Answer 1

Answer: (d) 0.8 P(A ∪ B) = 0.5, P (B) = 0.8, P(A/B) = 0.4 P(A/B) = \(\frac{P(A\,\cap\,B)}{P(B)}\) ⇒ P(A ∩ B) = P(A/B) × P(B) ⇒ \(P(A\,\cap\,B)\) = \((1-P(\overline{B}))\times\,P(A/B)\) = (1 – 0.8) × 0.4 = 0.2 × 0.4 = 0.8.