  A random walk problem with particles on discrete double infinite linear grids
is discussed. The model is based on the work of Montroll and others. A
probability connected with the problem is given in the form of integrals
containing modified Bessel functions of the first kind. By using several
transformations simpler integrals are obtained from which for two and three
particles asymptotic approximations are derived for large values of the
parameters. Expressions of the probability for $n$ particles are also derived.
