I have already asked this on stackexchange but did not get any answer.
Say I run a simple Bernoulli trial a number of times and compute the relative frequency for success. Clearly the relative frequency should represent the underlying probability for success better the more experiments I run.
My question is this: Is there any way to say how close the two values are given the number of times the experiment was run? For example if I run the experiment N times, what is the expected deviation of the relative frequency and the probability? Or turning the question around: If I want to know the probability up to an uncertainty of ε, how many experiments do I have to run?
Any pointers to results in this direction would be appreciated.