Question

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

P(A|B) = P(A∩B)P(B)=P(A)P(B)

Since P(B) ≠ 0, which means it is ≤ 1

Therefore, P (A/B) must be ≥ P(A).