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

Answer: (A)

$\frac{2}{5}$

Answer 2

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 = $\frac{^5C_2}{^5C_2 + {^6C_2}}$