$2$ integers are selected at random from $1$ to $11$.
If the sum of integers is even, what is the probability that both the numbers are odd?
I know that for the sum to be even, either both numbers have to be odd or both have to be even but how to find the probability?
Best Answer
You are looking for the probability that both numbers are odd given that their sum is even.
So, your sample space is the set of possibilities in which the sum is even: As you remark, this can be achieved with both numbers being odd or both being even. But how many total possibilities does this yield? Call that number $N$.
Next, how many of the possibilities in your sample space consist of two odd numbers? Call this total $n$, so that the probability is $n/N$.
This should be enough for you to work this through a bit further. For clarity's sake, though, it would be helpful if you specified in your question whether the two integers can be the same (e.g., $3$ and $3$) or whether they must be distinct from one another.