Two numbers are randomly selected from integers 1 through 9. What is the probability that only one of the integers is odd given that the sum of the two numbers is odd?

1/4

1

40/81

5/40

Another one where there's a danger of overthinking it!

The sum of ANY two integers is odd only if one is even and one is odd.

If they're both odd OR both even, then their sum is even.

So if their sum is odd, then one is odd and the other is even.

The probability is ' 1 ' (100%).