Question

Which is more likely: rolling a total of 8 when two dice are rolled or rolling a total of 8 when3 dice are rolled?

Answer 1

Proof.
For two dice, the number of favorable cases is 5: (6, 2);(5, 3);(4, 4);(3, 5);(2, 6); so the probability is 5/36 = 30/216
For three dice, the number of favorable cases is 21: (5, 2, 1), (4, 3, 1) counted with all permutations (so 6 2 = 12), and (1, 1, 6), (2, 2, 4), (3, 3, 2), counted with the distinct permutations (so 3 3 = 9). The probability is 21/216
So the more likely case is for two dice.