Posted by **Theo** on Sunday, January 29, 2012 at 3:56pm.

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.

- Math -
**Damon**, Sunday, January 29, 2012 at 4:07pm
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

- Math -
**Anonymous**, Monday, January 30, 2012 at 1:23am
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.

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