  Two infinite 0-1 sequences are called compatible when it is possible to cast
out 0's from both in such a way that they become complementary to each other.
Answering a question of Peter Winkler, we show that if the two 0-1-sequences
are random i.i.d. and independent from each other, with probability p of 1's,
then if p is sufficiently small they are compatible with positive probability.
The question is equivalent to a certain dependent percolation with a power-law
behavior: the probability that the origin is blocked at distance n but not
closer decreases only polynomially fast and not, as usual, exponentially.
