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If P(A|B) > P(A), then which of the following is correct ?

\[ \begin{array} ((A) \: P(B|A) \lt P(B) \quad & (B)\: P(A \cap B) \lt P(A) . P(B) \\ (C)\: P(B|A) \gt P(B) \quad & (D)\: P(B|A) = P(B) \end{array} \]

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Given $P \large(\frac{A}{B}) $$\gt P (B)$.
$\Rightarrow \large\frac{P (A\cap B)}{P(B)} $$\gt P (A) \rightarrow P (A \cap B) \gt P(A).P(B)$
$\Rightarrow \large\frac{P (A\cap B)}{P(A)} $$\gt P (B) \rightarrow P \large(\frac{B}{A}) $$\gt P (B)$.
answered Jun 22, 2013 by balaji.thirumalai

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