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

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.