**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 $=\frac{{ }^{5} \mathrm{C}_{2}}{{ }^{5} \mathrm{C}_{2}+{ }^{6} \mathrm{C}_{2}}$