  The density classification task is to determine which of the symbols
appearing in an array has the majority. A cellular automaton solving this task
is required to converge to a uniform configuration with the majority symbol at
each site. It is not known whether a one-dimensional cellular automaton with
binary alphabet can classify all Bernoulli random configurations almost surely
according to their densities. We show that any cellular automaton that washes
out finite islands in linear time classifies all Bernoulli random
configurations with parameters close to 0 or 1 almost surely correctly. The
proof is a direct application of a "percolation" argument which goes back to
Gacs (1986).
