Question 21
Dewa has a standard 6-sided fair die and a 6-sided unfair die, where each has 6 sides printed with little dots from 1, 2, 3, 4, 5, and 6. For the fair die, each of the outcomes when rolled is equally likely. While for the unfair die, each of the outcomes for a side to appear is proportional to the number of dots on its side. Dewa rolls both dice at the same time independently. If the probability that the sum of the dots on the sides that appear equals 4 is $\frac mn$ where the greatest common divisor of m and n is 1, then what is the value of $m+n$?