When a die is thrown twice, there are 36 possible outcomes.

3 of these outcomes give a sum of 4:

- 1 and 3
- 2 and 2
- 3 and 1

3 of these outcomes give a sum of 10:

- 4 and 6
- 5 and 5
- 6 and 4

Therefore, there are 6 outcomes that produce a sum of 4 or 10.

The probability is 6/36 = 1/6