  The list of physically motivated urn models that can be solved in terms of
classical orthogonal polynomials is very small. It includes a model proposed by
D. Bernoulli and further analyzed by S. Laplace and a model proposed by P. and
T. Ehrenfest and eventually connected with the Krawtchouk and Hahn polynomials.
This connection was reversed recently in the case of the Jacobi polynomials
where a rather contrived, and later a simpler urn model was proposed. Here we
consider an urn model going with the Jacobi-Pi\~neiro multiple orthogonal
polynomials. These polynomials have recently been put forth in connection with
a stochastic matrix.
