Two fair dice are thrown and the numbers are added. Which of these pairs of sums are equally likely?

Replacing each die score k by 7 − k pairs off the outcomes and turns a sum of s into a sum of 14 − s, so the sums s and 14 − s always occur equally often. Since 4 + 10 = 14, those two match, each arising in 3 ways. Checking the others: 5 and 8 arise in 4 and 5 ways, 6 and 9 in 5 and 4 ways, and 3 and 7 in 2 and 6 ways.