  We use the decoherent histories approach to quantum theory to compute the
probability of a non-relativistic particle crossing $x=0$ during an interval of
time. For a system consisting of a single non-relativistic particle, histories
coarse-grained according to whether or not they pass through spacetime regions
are generally not decoherent, except for very special initial states, and thus
probabilities cannot be assigned. Decoherence may, however, be achieved by
coupling the particle to an environment consisting of a set of harmonic
oscillators in a thermal bath. Probabilities for spacetime coarse grainings are
thus calculated by considering restricted density operator propagators of the
quantum Brownian motion model. We also show how to achieve decoherence by
replicating the system $N$ times and then projecting onto the number density of
particles that cross during a given time interval, and this gives an
alternative expression for the crossing probability. The latter approach shows
that the relative frequency for histories is approximately decoherent for
sufficiently large $N$, a result related to the Finkelstein-Graham-Hartle
theorem.
