I'm hoping for some help with this excericse in probability.
Let $V$ be a set and let $V'$ be a randomly chosen subset of $V$ such that each element belongs to $V'$ with probability $p$.
Now, let $S \subset V$ such that $|S|= x$, what's the probability that $|V' \cap S|<x/3$?
It might be easier to assume that $p=1/2$.
Thanks a lot.