  We show several results on convergence of the Monte Carlo method applied to
consistent approximations of the isentropic Euler system of gas dynamics with
uncertain initial data. Our method is based on combination of several new
concepts. We work with the dissipative weak solutions that can be seen as a
universal closure of consistent approximations. Further, we apply the
set-valued version of the Strong law of large numbers for general multivalued
mapping with closed range and the Koml\'os theorem on strong converge of
empirical averages of integrable functions. Theoretical results are illustrated
by a series of numerical simulations obtained by an unconditionally convergent
viscosity finite volume method combined with the Monte Carlo method.
