  Denote by $\mathcal{H}_k (n,p)$ the random $k$-graph in which each $k$-subset
of $\{1... n\}$ is present with probability $p$, independent of other choices.
More or less answering a question of Balogh, Bohman and Mubayi, we show: there
is a fixed $\varepsilon >0$ such that if $n=2k+1$ and $p> 1-\varepsilon$, then
w.h.p. (that is, with probability tending to 1 as $k\rightarrow \infty$),
$\mathcal{H}_k (n,p)$ has the "Erd\H{o}s-Ko-Rado property." We also mention a
similar random version of Sperner's Theorem.
