Two integers are selected at random from the set 1, 2, ...., 11.

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 :

Accepted Answer

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 = $${{{}^5{C_2}} \over {{}^5{C_2} + {}^6{C_2}}}$$ = $${2 \over 5}$$

Solutions · 1