You have two fair six-sided dice. One die has faces numbered 1 through 6, while the other die has faces numbered 7 through 12. What is the probability of rolling a sum greater than 15 when rolling both dice at once?
The probability of rolling a sum greater than 15 is 11/36.

Here's the reasoning:

1. There are a total of 6 * 6 = 36 possible outcomes when rolling both dice.
2. To get a sum greater than 15, the minimum roll on the first die is a 4 (since the maximum roll on the second die is 12, and 4 + 12 = 16).
3. When rolling a 4 on the first die, there are 3 possible rolls on the second die that result in a sum greater than 15: 10, 11, and 12.
4. Similarly, when rolling a 5 or 6 on the first die, there are 2 and 1 possible rolls on the second die, respectively, that result in a sum greater than 15.
5. So, there are a total of 3 + 2 + 1 = 6 successful outcomes out of 36 possibilities.
6. The probability of rolling a sum greater than 15 is therefore 6/36, which simplifies to 11/36.

So, the probability of rolling a sum greater than 15 is 11/36.