Question

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:

• A. $\frac{2}{5}$
• B. $\frac{1}{2}$
• C. $\frac{3}{5}$
• D. $\frac{7}{10}$

Answer 1

The correct option is A $\frac{2}{5}$

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 $=\frac{{}^5{C}_2}{{}^5{C}_2{+}^6{C}_2}$ = $\frac{2}{5}$