MathDB

When rolling a certain unfair six-sided die with faces numbered

1, 2, 3, 4, 5

, and

6

, the probability of obtaining face

F

is greater than

\frac{1}{6}

, the probability of obtaining the face opposite is less than

\frac{1}{6}

, the probability of obtaining any one of the other four faces is

\frac{1}{6}

, and the sum of the numbers on opposite faces is

7

. When two such dice are rolled, the probability of obtaining a sum of

7

\frac{47}{288}

. Given that the probability of obtaining face

F

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers, find

m+n

Problem Statement