Yeah, okay, my math was wrong, but I still sort of think your guys' is too. Shouldn't the probability of at least one crit be this:
(0.03*0.97*0.97*0.97*0.97)+(0.03*0.03*0.97*0.97*0.97)+(0.03*0.03*0.03*0.97*0.97)+(0.03*0.03*0.03*0.03*0.97)+(0.03*0.03*0.03*0.03*0.03)
As in, the chance of one crit, plus the chance of two crits, plus the chance of three crits, plus the chance of four crits, plus the chance of five crits. I think this should be significantly less than 14%. Google is telling me this is about 2.7% chance total, meaning I was right in my prediction that the chance of getting multiple crits was basically negligible compared to the chance of exactly one.
Ok i'll tell you exactly what you did there, you added the chance of one particular sequence to happen (for instance, one crit, then 4 non-crits) to the chance of one other particular sequence (example : one crit, 3 non-crits, then one crit), and so on, and what you have as a result is not really of use. What you gotta take into account if you do it that way, is the number of different possible sequences for that probability. The first part has 5 different sequences possible (depending on which hit you score the crit), the second part has 10 different sequences possible, the 3rd 10 as well, the 4th has 5 and the last one has only one sequence possible. To get the correct total probability, you have to do :
(5*0.03*0.97*0.97*0.97*0.97)+(10*0.03*0.03*0.97*0.97*0.97)+(10*0.03*0.03*0.03*0.97*0.97)+(5*0.03*0.03*0.03*0.03*0.97)+(0.03*0.03*0.03*0.03*0.03)
Then you get exactly 0,1412659743 (14.12659743%) chance to score at least one crit
(the same result i got with my method)
That's the reason why i calculated the chance of no crits instead, it's faster because there is only one possible sequence, and then you just do 1-(chance of no crit), and you get your chance of at least one crit.
Edit (You are also right in saying that scoring only one crit in the sequence makes up for most of the probability : out of those "0,1412659743", the probability to score only one crit is "0,1327939215")