Two fair dice are thrown and a friend reports, truthfully, that the two dice did NOT show the same number. Given only this, what is the probability that the two numbers add up to 7?

The report shrinks the sample space: of the 36 throws, the 6 doublets are ruled out, leaving 36 − 6 = 30 equally likely throws. Every throw adding to 7 — (1,6), (6,1), (2,5), (5,2), (3,4), (4,3) — already has unequal numbers, so 6 of the surviving 30 qualify: 6/30 = 1/5. Trap 1/6 = 6/36 ignores the information given and answers the unconditional question. Trap 6/35 shrinks the space by only one outcome instead of by all six doublets. Trap 1/30 keeps just one favourable throw.