Question

Let H1, …, Hn be mutually exclusive and exhaustive events with P(Hi) > 0, i = 1, 2, …, n. Let E be any other event with 0 < P(E) < 1.

Statement-1: P(Hi|E) > P(E |Hi)·P(Hi) for i = 1, 2, …, n. because

Statement-2: ∑P(Hi) for i∈[i=1, n] = 1.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

(C) Statement-1 is True, Statement-2 is False

(D) Statement-1 is False, Statement-2 is True

Answer 1

Answer is (D) Statement-1 is False, Statement-2 is True

Statement-1: If P(Hi ∩E) = 0 for some i, then

Hence, Statement-1 may not always be true.

Statement-2: Clearly, we can write as

Hence, Statement-2 is true.