  It is well known that a random subgraph of the complete graph $K_n$ has
chromatic number $\Theta(n/\log n)$ w.h.p. Boris Bukh asked whether the same
holds for a random subgraph of any $n$-chromatic graph, at least in
expectation. In this paper it is shown that for every graph, whose fractional
chromatic number is at least $n$, the fractional chromatic number of its random
subgraph is at least $n/(8\log_2(4n))$ with probability more than
$1-\frac{1}{2n}$. This gives the affirmative answer for a strengthening of
Bukh's question for the fractional chromatic number.
