a pair of fair dice is rolled. what is the probability of rolling a sum of 10? what are the odds against rolling a sum of 10?

Probability of rolling a sum of 10: 3 / 36 = 1 / 12 = 0.083. Odds against rolling a sum of 10: 11/12 = 0.917

Explanation:

1) Sample space:

There are 6 * 6 = 36 different combinations (sums) possible Of those these are the combinations that sum 10:

4 + 6, 5 + 5, and, 6 + 4

Hence, there are 3 different combinations that sum 10, and the proba bility of rolling one of them is:

2) Probability of rolling a sum of 10 = number of combinations that sum 10 / number of total possible combinations

Probability of rolling a sum of 10 = 3 / 36 = 1 / 12 = 0.083.

3) The odds against rolling a sum of 10 is the complement, this is 1 - 1/12 = 11/12 = 0.917