Let X and Y are two events such that P(X Y) = P(X Y). Statement 1: P(X Y') = P(X' Y) = 0 Statement 2: P(X) + P(Y) = 2P(X Y)

JEE Main 2012 Mathematics question

Let X and Y are two events such that . Statement 1: Statement 2:

(1)Statement 1 is false, Statement 2 is true.
(2)Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.Correct
(3)Statement 1 is true, Statement 2 is false.
(4)Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.

Answer: (2)

means the events coincide up to probability zero: , and similarly —

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Question ID VK-103430