Let's say I have a probability distribution $F(x)$, which is a cdf.
Then, I have a value $y$ at some place on the support of $F$.
Then, there will be some number $n$ random independent draws from $F$, and I want to know the probability that at least one of them is $> y$.
I would think that to find this I would do $n(1-F(y))$, since the pr. of any one draw being $> y$ is $1-F(y)$. But say $F(y)$ is $.5$. Then, is $n=3$, then I would get $1.5$, which of course doesn't make any sense.
What am I doing wrong?