Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.

Out of integers from 1 to 11, there are 5 even integers and 6 odd integers. Consider the following events:

            A = Both the numbers chosen are odd,

            B = the sum of the numbers chosen is even,

∴ Required probability = P(A/B)

= Probability that the two numbers chosen are odd if it is given that the sum of the numbers chosen is even.