How do you work out the probability of dice problems?

Count the number of permutations of the expected results and divide by the number of permutations of the possible results. This is standard probability theory, and it applies to everything in probability, not just dice.

For instance, with two dice, there are 36 possible permutations, while there is only 1 permutation that adds up to a sum of 2, though there are 6 permutations that add up to a sum of 7. As a result, the probability of rolling a sum of 2 is 1 in 36, while rolling a 7 is 6 in 36, or 1 in 6.