Question

Roszena rolls two standard six-sided dice. If the sum of the numbers on the top faces is not 6, what is the probability that the sum is 7? Express your answer as a rational number in lowest terms.

Answer 1

The number of combinations that does NOT sum up to 6 is 31. (1-1,1-2,1-3,1-4,1-6;2-1,2-2,2-3,2-5,2-6; 3-1,3-2,3-4,3-5,3-6;4-1,4-3,4-4,4-5,4-6;
5-2,5-3,5-4,5-5,5-6;6-1,6-2,6-3,6-4,6-5, and 6-6)
Six of those combinations add up to 7. Therefore the probability is 6/31.