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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?

 Feb 3, 2018
 #1
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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%  

 

 

cool cool cool

 Feb 3, 2018
 #2
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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.

 Feb 3, 2018

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