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Q.

If P(A/B)>P(A), then which of the following is correct:

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a

$P (B ∣ A) < P (B)$

b

$P (A \cap B) < P (A) \cdot P (B)$

c

$P (B ∣ A) > P (B)$

d

$P (B ∣ A) = P (B)$

answer is C.

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Detailed Solution

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$\begin{array}{l} P (A ∣ B) > P (A) \\ \Rightarrow \frac{P (A \cap B)}{P (B)} > P (A) \\ \Rightarrow P (A \cap B) > P (A) \cdot P (B) \end{array} \begin{array}{l} \Rightarrow \frac{P (A \cap B)}{P (A)} > P (B) \\ \Rightarrow P (B ∣ A) > P (B) \end{array}$

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