By Borel-Cantelli's lemma (part I), we have . By taking the complement, we get that
This means that .
Then you have to get the epsilon into the probability, and I think you have to assume first that epsilon is rational (so that there is a countable number of epsilon's).
I don't really remember how to do and I have to go out right now, I'll try to think about it, unless you do before me