To solve this problem, let's first determine the possible outcomes when two dice are thrown together. Each die has 6 faces, so the total number of possible outcomes is \( 6 \times 6 = 36 \).

Now, we need to find the number of outcomes where the sum is at least 10. The possible outcomes that sum to 10, 11, or 12 are:

- Sum of 10: (4, 6), (5, 5), (6, 4) → 3 outcomes
- Sum of 11: (5, 6), (6, 5) → 2 outcomes
- Sum of 12: (6, 6) → 1 outcome

Adding these up, we have \( 3 + 2 + 1 = 6 \) favorable outcomes.

The probability of obtaining at least a score of 10 is then given by the ratio of favorable outcomes to the total number of outcomes:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6}
\]

Thus, the correct answer is A. 1/6.