Question

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

1. P(A ∩ B)
2. P(A|B)
3. P(A ∪ B)

Answer 1

(i) Given P(B|A) = 0.4

⇒ `(P (A cap B))/(P(A)) = 0.4`

⇒ P(A ∩ B) = P (A) × 0.4

= 0.8 × 0.4

= 0.32

(ii) `P(A|B) = (P (AcapB))/(P(B))`

`= 0.32/0.5`

= 0.64

(iii) P(A ∪ B) = P (A) + P (B) - P (A ∩ B)

= 0.8 + 0.5 - 0.32

= 1.3 - 0.32

= 0.98