If it's

*not*1 on both rolls, then the higher roll is taken. So if the d4 rolls a 3 and the d10 rolls a 1, the result is 3. If the d4 rolls a 12 and the d10 rolls 11, it's 12. But at this point I don't know what the odds of rolling exactly 2 are, or exactly 3, or 4, or 12, or 22. I don't know how to figure that out. The probabilities of at least X would then be a simple matter of the 100-(Probability of X-1). But how do I figure out what the odds of getting exactly each of those numbers is?

Running a small program

*without*the exploding dice (which is easier), I find that the values are as follows:

1 - 2.5%

2 - 7.5%

3 - 12.5%

5 - 17.5%

6 - 10%

7 - 10%

8 - 10%

9 - 10%

10 - 10%

I can't figure out how to get

*those*numbers, either (without running through all possibilities, which I can't do with the exploding dice).