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Question:

Let A and E be any two events with positive probabilities. Statement - 1 : P(E|A) ≥ P(A|E)P(E). Statement - 2 : P(A|E) ≥ P(A∩E). Both the statement are true. Both the statement are false. Statement - 1 is true, Statement - 2 is false. Statement - 1 is false, Statement - 2 is true.

Statement - 1 is true, Statement - 2 is false

Statement - 1 is false, Statement - 2 is true.

Both the statement are true

Both the statement are false

Solution:

P(E|A) = P(E∩A)/P(A)
P(A|E) = P(E∩A)/P(E)
0 ≤ P(E) ≤ 1
P(A|E) ≥ P(E∩A)
P(E|A) = P(A|E)P(E)/P(A).
0 ≤ P(A) ≤ 1
So, P(E|A) ≥ P(A|E)P(E)