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

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

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1 Answer

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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 by poojasapani_1
edited Jun 19, 2013 by balaji.thirumalai

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