  Let $F$ be a group whose abelianization is $\Z^k$, $k\geq 2.$ An element of
$F$ is called visible if its image in the abelianization is visible, that is,
the greatest common divisor of its coordinates is 1.
  In this paper we compute three types of densities, annular, even and odd
spherical, of visible elements in surface groups. We then use our results to
show that the probability of a homogeneous equation in a surface group to have
solutions is neither 0 nor 1, as the lengths of the right- and left-hand side
of the equation go to infinity.
