The faces of two regular dodecahedra are labeled with the numbers 1 to 12 in order to make dice. If these dice are rolled, what is the probability that the sum of the two top numbers is greater than 12?
There are 12^2 = 144 possible outcomes
Outcome Freq
2 1
3 2
4 3
5 4
6 5
7 6
8 7
9 8
10 9
11 10
12 11
Sum of 66
Freq
So.....the sum of the frequencies for rolling a number > 12 = 144 - 66 = 78
So...the probability of rolling a number 12 or greater = 78/144 = 13/24 ≈ 54.16%
Sum of arithmetic series from 1 to 12 =[F+L] /2 x N =[1+12] / 2 x 12 =78 combinations of 13 to 24
So, the probability is =78 /(12^2) =78 / 144.
