Question

Compute the odds in favor of rolling a sum of 10 in a single roll of two fair dice

Answer 1

There are 6 possibilities for the outcome of one cube.  For each of those . . .
There are 6 possibilities for the outcome of the other cube.

Total possibilities for the roll of 2 cubes = (6 x 6) = 36 outcomes.

Ways to roll a sum of 10:
4 . . . 6
5 . . . 5
6 . . . 4
Three possibilities.

Probability of rolling a 10 = 3/36 = 1/12 = 8 and 1/3 percent 

Odds in favor of success = 1 in 12 , or    1 to 11 . (11 to 1 odds of failing.)