Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find (i) P(A ∩ B) (ii) P(A ∪ B) (iii) P (A|B) (iv) P (B|A)

Question

Philoid · Accepted Answer

Given: P(A) = 0.3 and P(B) = 0.4

(i) P(A ∩ B)

When A and B are independent.

⇒ P (A ∩ B) = P(A) . P(B)

⇒ P (A ∩ B) = 0.3 × 0.4

⇒ P (A ∩ B) = 0.12

(ii) P(A ∪ B)

As we know, P (A ∪ B) = P(A) + P(B) - P (A ∩ B)

⇒ P (A ∪ B) = 0.3 + 0.4 – 0.12

⇒ P (A ∪ B) = 0.58

(iii) P (A|B)

As we know

⇒

⇒ P (A|B) = 0.3

(iv) P (B|A)

As we know

⇒

⇒ P (B|A) = 0.4