Two different numbers are picked at random from 1, 2, 3, 4, 5, 6, 7, 8, 9. What is the probability that their sum is even?

Two of the nine numbers can be picked in C(9,2) = 36 ways. A sum is even only when both numbers are odd or both are even, which happens in C(5,2) + C(4,2) = 10 + 6 = 16 ways, so the probability is 16/36 = 4/9. The complement 5/9 = 20/36 belongs to an ODD sum, and odd sums are genuinely the likelier ones here because the list holds one more odd number than even. That is exactly why 1/2 is wrong — even and odd sums would balance only if the two kinds of number were equally many. Keeping the both-odd case alone gives 10/36 = 5/18.