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  4. Two integers are selected at random from the set 1, 2,...., 11. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :

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Q. Two integers are selected at random from the set {1, 2,...., 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :

JEE MainJEE Main 2019Probability - Part 2

Solution:

Since sum of two numbers is even so either both are odd or both are even. Hence number of elements in reduced samples space
$ = {^5C_2} + {^6C_2} $
so required probability = $ \frac{^5C_2}{^5C_2 + {^6C_2}}$