Assume you are rolling two dice; the first one is red, and the second one is green. Use a systematic listing to determine the number of ways you can roll a total of 10 on the two dice.

Step 1 ：First, we need to understand the problem. We are rolling two dice, one red and one green, and we want to find the number of ways we can roll a total of 10 on the two dice.

Step 2 ：Next, we need to list all the possible outcomes that sum up to 10. The possible outcomes are: (4,6), (5,5), (6,4) for the red and green dice respectively.

Step 3 ：Each outcome is an independent event, so we count each outcome separately. There are 3 successful outcomes.

Step 4 ：Rolling each die is also an independent event, so we multiply the 6 possible outcomes for the red die by the 6 possible outcomes for the green die, to get 36 total outcomes.

Step 5 ：Hence, the number of ways to roll a total of 10 on the two dice is 3 out of 36.

Step 6 ：Finally, we simplify the fraction \(\frac{3}{36}\) to get \(\boxed{\frac{1}{12}}\).