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Misc 18 - If P(A|B) > P(A), which is correct - NCERT - Miscellaneous

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  1. Chapter 13 Class 12 Probability
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Misc 18 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) Given P(A|B) > P(A) 𝑃(𝐴 ∩ 𝐵)﷮𝑃(𝐵)﷯>P(A) P(A ∩ B) < P(A) . P(B) Finding P(B|A) P(B|A) = 𝑃(𝐴 ∩ 𝐵)﷮𝑃(𝐴)﷯ From (1) P(A ∩ B) < P(A) . P(B) P(A ∩ B) < P(A) . P(B) Dividing by P(A) both sides 𝑃(𝐴 ∩ 𝐵)﷮𝑃(𝐴)﷯> 𝑃 𝐴﷯. 𝑃 𝐵﷯﷮𝑃(𝐴)﷯ P(B|A) > P(B) So, C is the correct answer.

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