Probability of an event in n tries

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Delta2
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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.
 

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Charles Link
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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 ##.
 
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StoneTemplePython
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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}##
 
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Delta2
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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.
 
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