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 \(18\)?
+36 First we need to find a list of what numbers from both sets {1,2,3,4,5,6,7,8,9,10,11,12} and {1,2,3,4,5,6,7,8,9,10,11,12} will add up to 19 or greater. These are:
12+7=19
12+8=20
12+9=21
12+10=22
12+11=23
12+12=24
11+8=19
11+9=20
11+10=21
11+11=22
10+9=19
10+10=20
This amounts to 12 combinations. Since this can happen on opposite dice, we multiply by 2 to get 24 outcomes. The total number of outcomes are 12*12=144. So, the answer is 24/144 = 1/6.
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