Two fair dice are thrown and the numbers are added. Which is likelier — that the sum is a multiple of 3, or that the sum is a multiple of 4 — and with what probability?

Multiples of 3 are the sums 3, 6, 9 and 12, arising in 2 + 5 + 4 + 1 = 12 of the 36 outcomes, a probability of 12/36 = 1/3. Multiples of 4 are the sums 4, 8 and 12, arising in 3 + 5 + 1 = 9 outcomes, a probability of 9/36 = 1/4. So the multiple of 3 is likelier. Counting the SUMS (four of them against three) instead of the outcomes behind them is the usual trap.