  With the aid of simple analytical computations for the Ehrenfest model, we
clarify some basic features of macroscopic irreversibility. The stochastic
character of the model allows us to give a non-ambiguous interpretation of the
general idea that irreversibility is a typical property: for the vast majority
of the realizations of the stochastic process, a single trajectory of a
macroscopic observable behaves irreversibly, remaining "very close" to the
deterministic evolution of its ensemble average, which can be computed using
probability theory. The validity of the above scenario is checked through
simple numerical simulations and a rigorous proof of the typicality is provided
in the thermodynamic limit.
