Two integers are selected at random from integers 1 through 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.

Since the sum of the integers is even if either both are even or both are odd.