MathDB

Jim has two fair

6

-sided dice, one whose faces are labelled from

1

6

, and the second whose faces are labelled from

3

8

. Twice, he randomly picks one of the dice (each die equally likely) and rolls it. Given the sum of the resulting two rolls is

9

, if

\frac{m}{n}

is the probability he rolled the same die twice where

m, n

are relatively prime positive integers, then what is

m + n

Problem Statement