Let's say there is an event $A$, so that $P(A)=\frac{1}{n}$.
People are mostly saying;
"In average, if you will try $n$ times, the event will accor once".
For example, if the probability to win some game is one to a milion, then you should play a milion times in order to win.
But in fact, the win if you play a milion times, is not so guaranteed, and for $n$ that is getting big, the probability is about $63.21\%$, because;$$\lim_{n\to \infty}1-\left(1-\frac{1}{n}\right)^n=1-\frac{1}{e}\approx 0.6321$$So my question is, is the first statement wrong?
Best Answer
Of course you are right about the probability while trying $n$ times. But the initial statement is still correct.
The statement says that if you will try $n$ times, and another $n$ times, until you get many sets of $n$ times trying; in average, you will succeed $1$ time out of each such series. That is cold Expactation.