While developing the mechanics for a game in the works, I'm trying to make everything as mathematically even as possible. However, I need help with a problem I can't seem to figure out.

Obviously the chances of rolling a 4 on a 4-sided die is 25%. My question is, what is the chance of rolling at LEAST, for example, one 4 on two 4-sided dice, or three 4-sided dice, etc. The way I'm doing skills is the NUMBER of dice you roll. Quick example... say one guy is good at climbing, and another one is not so good, and both are trying to climb a cliff. Both have a target number of 4. The first guy has a 5 in climbing, while the second guy has a 1. How much better are the first guys chances of rolling at least one 4 (on five dice), than the individual who just has one die to roll a 4? I'm sure there's a formula out there... and it's not limited to just 4 siders, either. I just used them for simplicity's sake in the examples. Any help would be MUCH appreciated! Thanks!

I can't remember it but I do know there is a proven mathematical forumla for this. If I think of it I will let you know.