A full set of dominoes has 28 tiles, one for every unordered pair of numbers from 0 to 6, doubles included. One tile is drawn at random. What is the probability that the two numbers on it add up to 6?

List the tiles whose two numbers total 6: 0-6, 1-5, 2-4 and the double 3-3. That is 4 tiles out of 28, a probability of 4/28 = 1/7. The value 3/28 leaves out the double 3-3, which is easy to miss because it is the only tile of the four with a repeated number. The value 1/4 = 7/28 is the probability of drawing a double, since the doubles 0-0 to 6-6 number 7 — a different question about the same set. The value 1/9 = 4/36 treats the set as $6\times 6=36$ tiles, which both forgets that 0 is one of the seven numbers and counts 1-5 and 5-1 as two different tiles when a domino has no direction.