I Probability of an event in n tries

[Delta2]

IF the probability for an event to happen in one try is m/n , what is the probability for the event to happen at least one time in n successive tries. In each try the probability of event is m/n.

I care mainly for the formula that I suppose it involves m and n but if you kind enough to provide the reasoning it is welcomed.

 

[Charles Link]

If you use the probability $p$, the probability it won't happen in $n$ tries is $(1-p)^n$ and so the probability of one or more occurrences is $P=1-(1-p)^n$.

 

[StoneTemplePython]

I'm not sure if it is worth point this out, but for large n

$1 - (1-p)^n = 1 - (1-\frac{m}{n})^n \approx 1 - e^{-m}$

 

[Delta2]

Thanks both I couldn't imagine it was so simple, I was thinking it the hard way (computing the probability for the event to appear exactly k times and then summing from k=1 to n). I also was thinking of a way to remove the dependence of n from the formula, so thanks @StoneTemplePython too.