Sam rolls a standard die, and then Ruth rolls the same die. The probability that Ruth's number is higher than Sam's can be written as a/b where a and b have no common factors greater than 1. Find a.

Answer 1

There are six numbers, 36 boxes below
* 1 2 3 4 5 6 Sam
1
2 *
3 * *
4 * * *
5 * * * *
6 * * * * *
Ruth
(5 + 4 + 3 + 2 +1)/36 = 15/36 = 5/12

Answer 2

5. The probability that both Sam’s
and Ruth’s roll produce the same result
is 1/6. The likelihood that Ruth has the
higher number is the same as the likelihood that Sam has the higher number.
Thus, we divide the remaining 5/6 in
half to get 5/12; the numerator is 5.