If P(A | B) P(A),then which of the followin | vedclass

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(B) Given that $P(A | B) > P(A)$.By the definition of conditional probability,we have $P(A | B) = \frac{P(A \cap B)}{P(B)}$.Substituting this into the

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$P(B | A) > P(B)$

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(B) Given that $P(A | B) > P(A)$.By the definition of conditional probability,we have $P(A | B) = \frac{P(A \cap B)}{P(B)}$.Substituting this into the inequality,we get $\frac{P(A \cap B)}{P(B)} > P(A)$.Multiplying both sides by $P(B)$ (assuming $P(B) > 0$),we get $P(A \cap B) > P(A) \cdot P(B)$.Now,dividing both sides by $P(A)$ (assuming $P(A) > 0$),we get $\frac{P(A \cap B)}{P(A)} > P(B)$.By the definition of conditional probability,$\frac{P(A \cap B)}{P(A)} = P(B | A)$.Therefore,$P(B | A) > P(B)$.Thus,the correct option is $B$.

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

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