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)

Question

Philoid · Accepted Answer

Given: P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4

(i) We know that

By definition of conditional probability,

⇒ P(A ∩ B) = P(B|A) P(A)

⇒ P(A ∩ B) = 0.4 × 0.8

⇒ P(A ∩ B) = 0.32

(ii) We know that

By definition of conditional probability,

⇒ P(A|B) = 0.64

(iii) Now, ∵ P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

⇒ P(A ∪ B) = 0.8 + 0.5 – 0.32 = 1.3 – 0.32

⇒ P(A ∪ B) = 0.98