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

$\begin{array} ((A) P(A|B)= \frac{P(B)}{P(A)} \quad & (B) P(A|B) < P(A) \\ (C) P(A|B) ≥ P(A) \quad & (D) None\: of\: these \end{array}$

If A $\subset$ B, then A $\cap$ B = A.
P(A|B) = $\large\frac{P (A \cap B)}{P(B)} = \frac{P(A)}{P(B)}$
Since P(B) $\neq$ 0, which means it is $\leq$ 1.
Therefore, P (A|B) must be $\geq$ P(A).
answered Mar 8, 2013
edited Jun 19, 2013