First the probability that they show the same is 1/6 (there are 6 equally likely

way that they can be equal out of a total of 36 equally likely outcomes).

So the probability that they are not the same is 5/6. Also symmetry

guarantees that the probability that red die shows a larger number than the

green is the same as vice versa, and these must sum to 5/6.

Hence the probability that the red shows larger than the green is 5/12.

RonL