JEE MAIN - Mathematics (2019 - 11th January Morning Slot - No. 18)
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 :
$${2 \over 5}$$
$${1 \over 2}$$
$${7 \over 10}$$
$${3 \over 5}$$
Explanation
Since sum of two numbers is even so either both are odd or both are even. Hence number of elements in reduced samples space = 5C2 + 6C2
So, required probability = $${{{}^5{C_2}} \over {{}^5{C_2} + {}^6{C_2}}}$$ = $${2 \over 5}$$
So, required probability = $${{{}^5{C_2}} \over {{}^5{C_2} + {}^6{C_2}}}$$ = $${2 \over 5}$$
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