Let E and F be two independent events. The probability that exactly one of them occurs is 11 25 and the probability of none of them occurring is 2 25 . If P(T) denotes the probability of occurrence of the event T, then

JEE Advanced 2011 Mathematics question

Let E and F be two independent events. The probability that exactly one of them occurs is and the probability of none of them occurring is . If P(T) denotes the probability of occurrence of the event T, then

(A), Correct
(B),
(C),
(D), Correct

Answer: (A),(D)

Solution

Let , . Independence gives: none occurs: ; exactly one occurs: . From the first, ; subtracting the second: , and then $x +

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Question ID VK-025993