Assuming we have an array with $n$ Elements and want to find an unique element by randomly (uniformly) choosing. What would be the average case runtime?
My thoughts so far:
The chance to find the element is $\frac{1}{n}$ in every step. Thus, to find the element after $k$ steps is $(\frac{1}{n})^k$. Now we can calculate the expected value and get $\frac{n}{(n-1)^2}$. But: that doesn't really make as it returns results $< 1$ for $n > 2$.