If P (A|B) > P (A), then which of the following is correct: (A) P (B|A) < P (B) (B) P (A ∩ B) < P (A).P (B) (C) P (B|A) > P (B) (D) P (B|A) = P (B)

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Solution

It is given that, P( A|B )>P( A ) .

Apply the formula for conditional probability.

P( A|B )>P( A ) P( A∩B ) P( B ) >P( A ) P( A∩B )>P( A )⋅P( B ) P( A∩B ) P( A ) >P( B ) Further, simplify the above inequality.

P( B|A )>P( B ) Thus, out of all the four options, option (C) is correct.

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Similar questions

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

(A) P (B|A) < P (B) (B) P (A ∩ B) < P (A).P (B)

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

$(a) P (\frac{A}{B}) = \frac{P (A)}{P (B)} (b) P (\frac{A}{B}) < P (A) (c) P (\frac{A}{B}) \geq P (A) (d) N o n e o f t h e s e$

P (A / B) > P (A)

P (B / A) > P (B)

P (A / B) = \frac{P (A \cap B)}{P (B)}

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