Question

Two dice appear to be normal dice with their faces numbered fromto, but each die is weighted so that the probability of rollingthe numberis directly proportional to. The probability of rolling awith this pair of dice is, whereand are relativelyprime positive integers. Find

Answer 1

It is easier to think of the dice as $21$ sided dice with $6$ sixes, $5$ fives, etc. Then there are $21^2=441$ possible rolls. There are $2\cdot(1\cdot 6+2\cdot 5+3\cdot 4)=56$ rolls that will result in a seven. The odds are therefore $\frac{56}{441}=\frac{8}{63}$.

The answer is $8+63= {071}