Define $G(n, p)$ as a random directed graph ($n$ vertices; we put edge between two vertices with probability $p$).
What are the known results for the following problem:
Fix two vertices $v$ and $u$. What is the probability that there is at least a path (of length at most $k$) between $u$ and $v$? (clearly the result should be a function of $n$, $p$ and $k$). Upper-bound would work too, if there is no known exact answer.