Question

If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is true?

(A) P(A/B) = \(\frac{P(B)}{P(A)}\)

(B) P(A/B) < P(A)

(C) P(A/B) ≥ P(A)

(D) None of these

Answer 1

A ⊂ B ⇒ A ∩ B = A ⇒ P(A ∩ B) = P(A)

∴ P(A/B) = \(\frac{P(A∩B)}{P(B)}\)

= \(\frac{P(A)}{P(B)}\)

But P(B) ≤ 1

⇒ P(A/B) ≥ P(A).