Chance of success after multiple attempts.

[Kasseo]

Ok, so, this has probably been asked about 50 times, but I just can't find it, because I don't really know how to phrase the problem properly for the search engine.

So, following:

Chance of event occurring is 2% (aka a 50 sided die rolling a natural 1). How to calculate the probability of the event occurring once after multiple attempts? So let's say I roll 10d50, meaning it's 10 times a 2% chance. The only thing I remember from school is that it's not 20%, since that would lead to 100% at 50d50, which in term is Gambler's Fallacy and not actual math XD

Thanks for the help in advance.

 

[Romsek]

google Binomial Distribution

 

[Kasseo]

Yeah...no clue how the heck to even read that formula, but I've found a calculator by looking for Binomial Distribution. Thanks^^

 

[tkhunny]

I'm thinking you'll have better success with the Negative Binomial. It's more of a Survival Function.

p = probability of success
q = 1-p

p(1st roll) = p
p(2nd roll) = q*p
p(3rd roll) = q*q*p = q^2 * p
...
p(50th roll) = q^49 * p
...
etc.