Find the probability of not rolling a sun of 5

Answer 1

Assuming there are two dice, there are 36 different possible sums:

1-1, 1-2, 1-3, 1-4, 1-5, 1-6 and

2-1, 2-2, 2-3, 2-4, 2-5, 2-6 and

3-1, 3-2, 3-3, 3-4, 3-5, 3-6 and

4-1, 4-2, 4-3, 4-4, 4-5, 4-6 and

5-1, 5-2, 5-3, 5-4, 5-5, 5-6 and

6-1, 6-2, 6-3, 6-4, 6-5, 6-6

The rolls that add to five are 1-4, 2-3, 3-2, and 4-1 so there are 4 rolls that add to five.

That means there are 32 rolls that do not add to five (because there are 36 total possible rolls).

So the probability of not rolling a sum of 5 is 32/36 (which can be reduced to 8/9) or, written in percent, 88.9%