Let H_1, H_2, , H_n be mutually exclusive and exhaustive events with P(H_i) > 0, i = 1, 2, …, n. Let E be any other event with 0 P(E ,| ,H_i) P(H_i) for i = 1, 2, …, n. because STATEMENT-2 : _ i=1 ^ n P(H_i) = 1.

JEE Advanced 2007 Mathematics question

Let be mutually exclusive and exhaustive events with , i = 1, 2, …, n. Let E be any other event with 0 < P(E) < 1. STATEMENT-1 : for i = 1, 2, …, n. because STATEMENT-2 : .

(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 TrueCorrect

Answer: (D)

Solution

Statement-2 is true because the are mutually exclusive and exhaustive. Statement-1: , and since P(E) < 1 this exceeds only when

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Question ID VK-037457