Question

If P(A) = 0.8, P(B) = 0.5 and P(B/A) = 0.4, find

(i) P(A ∩ B)

(ii) P(A/B)

(iii) P(A ∪ B)

Answer 1

(i) P(B/A) = $\frac{P(A\cap B)}{P(B)}$ ⇒ 0.4 = $\frac{P(A\cap B)}{0.8}$
∴ P(A ∩ B) = 0.4 × 0.8 = 0.32.

(ii) P(A/B) = $\frac{P(A\cap B)}{P(B)}$ = $\frac{0.32}{0.5}$ = $\frac{32}{50}$ = $\frac{16}{25}$.

(iii) P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= 0.8 + 0.5 – 0.32 = 1.30 – 0.32
= 0.98.