To find the probability that the sum of two dice is greater than 10, follow these steps:

1. Determine the Total Number of Possible Outcomes:
- Each die has 6 faces.
- Therefore, the total number of outcomes when two dice are thrown is:
\[
6 \times 6 = 36
\]

2. Determine the Favorable Outcomes (sum greater than 10):
- The possible sums greater than 10 are 11 and 12.

For sum = 11:
- The possible outcomes are (5,6) and (6,5).
- Total outcomes for sum = 11: 2

For sum = 12:
- The only possible outcome is (6,6).
- Total outcomes for sum = 12: 1

Total favorable outcomes:
\[
2 + 1 = 3
\]

3. Calculate the Probability:
- Probability of the sum being greater than 10:
\[
\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} = \frac{3}{36} = \frac{1}{12}
\]

The probability that the sum of the two numbers obtained is greater than 10 is \(\frac{1}{12}\).

The correct answer is A. 1/12.