Probability- Calculus

Question

Find the probability that when two 8 sided dice are rolled, the sum of the numbers on the top faces is greater than 13.

Answer 1

Two dice are numbered 1 through 8

64 possible combinations (sums in the middle)

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8 9

2 3 4 5 6 7 8 9 10

3 4 5 6 7 8 9 10 11

4 5 6 7 8 9 10 11 12

5 6 7 8 9 10 11 12 13

6 7 8 9 10 11 12 13 14

7 8 9 10 11 12 13 14 15

8 9 10 11 12 13 14 15 16

6 of those sums are greater than 13 (14, 14, 15, 14, 15, 16)

so the probability of the sum of the two die being greater than 13 is 6/64 = 3/32