Question:
Let A and E be any two events with positive probabilities :
Statement - 1 : \(P(E/A)\ge P(A/E)P(E)\)
Statement - 2 : \(P(A/E)\ge P(A\cap E)\).
Let A and E be any two events with positive probabilities :
Statement - 1 : \(P(E/A)\ge P(A/E)P(E)\)
Statement - 2 : \(P(A/E)\ge P(A\cap E)\).
Statement - 1 : \(P(E/A)\ge P(A/E)P(E)\)
Statement - 2 : \(P(A/E)\ge P(A\cap E)\).
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Express both sides in terms of \(P(A\cap E)\) and use \(P(A),P(E)\le1\).
Updated On: Nov 11, 2026
- Both the statements are true
- Both the statements are false
- Statement - 1 is true, Statement - 2 is false
- Statement - 1 is false, Statement - 2 is true.
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The Correct Option is A
Solution and Explanation
\(P(A/E)P(E)=P(A\cap E)\) and \(P(E/A)=\frac{P(A\cap E)}{P(A)}\).
Statement 1: \(\frac{P(A\cap E)}{P(A)}\ge P(A\cap E)\) holds since \(0<P(A)\le1\). True.
Statement 2: \(P(A/E)=\frac{P(A\cap E)}{P(E)}\ge P(A\cap E)\) holds since \(0<P(E)\le1\). True.
Both statements are true.
Answer: (1) Both the statements are true
Statement 1: \(\frac{P(A\cap E)}{P(A)}\ge P(A\cap E)\) holds since \(0<P(A)\le1\). True.
Statement 2: \(P(A/E)=\frac{P(A\cap E)}{P(E)}\ge P(A\cap E)\) holds since \(0<P(E)\le1\). True.
Both statements are true.
Answer: (1) Both the statements are true
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