  We calculate the free energy of the disordered urn model using the law of
large numbers. It is revealed that the saddle point equation obtained by the
usage of the law of large numbers is the same as that obtained by the replica
method. Hence, we conclude that the replica symmetric solution is adequate for
the disordered urn model. Furthermore, we point out the mathematical similarity
of free energies between the urn models and the Random Field Ising Model; this
similarity gives an evidence that the replica symmetric solution of the urn
models is exact.
