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 16?

Guest Jun 22, 2022

#1**0 **

There are 12 x 12 = 144 ways to roll the 2 numbers.

Let's count the amount of ways as shown:

max digit = 12: (12, 5 - 12) = 8 ways

max digit = 11: (11, 6 - 11) = 6 ways

max digit = 10: (10, 7 - 10) = 4 ways

max digit = 9: (10, 8 - 9) = 2 ways

There are 8+6+4+2 = 20 ways, which makes for a probability of \({20 \over 144} = \color{brown}\boxed{ 5 \over 36 } \)

BuilderBoi Jun 22, 2022