Given an integer n, and an event n that happens with $P(\frac{1}{n})$, is the probability that e will happen in n trials bounded by any constant?
For example, if I had an n-sided fair die and a target value t, can I say with certainty that regardless of the value of n, the odds of rolling a t in n rolls are no worse than $\frac{1}{x}$ for some constant x?