Question:
Two integers are selected at random from the set $\{1,2, \ldots, 11\}$. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is :
Correct Option: 1
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
$={ }^{5} C_{2}+{ }^{6} C_{2}$
so required probability $=\frac{{ }^{5} \mathrm{C}_{2}}{{ }^{5} \mathrm{C}_{2}+{ }^{6} \mathrm{C}_{2}}$
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