  Consider any fixed graph whose edges have been randomly and independently
oriented, and write $\{S \leadsto i\}$ to indicate that there is an oriented
path going from a vertex $s \in S$ to vertex $i$. Narayanan (2016) proved that
for any set $S$ and any two vertices $i$ and $j$, $\{S \leadsto i\}$ and $\{S
\leadsto j\}$ are positively correlated. His proof relies on the
Ahlswede-Daykin inequality, a rather advanced tool of probabilistic
combinatorics.
  In this short note, I give an elementary proof of the following, stronger
result: writing $V$ for the vertex set of the graph, for any source set $S$,
the events $\{S \leadsto i\}$, $i \in V$, are positively associated -- meaning
that the expectation of the product of increasing functionals of the family
$\{S \leadsto i\}$ for $i \in V$ is greater than the product of their
expectations.
