# 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 ?

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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

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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.