I'm not really a statistics guy though, and couldn't wrap my head around calculating combinatorial weighted odds of dependent events (but if you're someone who understands calculating that kind of probability, please do weigh in!). So, I wrote a small program to simulate the modifier-rolling process, and drew some conclusions. The program (and raw results) are on GitHub.

I just wanted to point out that simulation is a perfectly acceptable way to come up with probabilities for a problem like this. Some problems don't have a closed form solution and might require simulation, but even in cases where an exact solution exists if the problem is complex you can get reasonable approximations via simulation.