Once again the problem of indistinguishability has been recently tackled. The question is why indistinguishability, in quantum mechanics but not in classical one, forces a changes in statistics. Or, what is able to explain the difference between classical and quantum statistics? The answer given regards the structure of their state
spaces: in the quantum case the measure is discrete whilst in the classical case it is continuous. Thus the equilibrium measure on classical phase space is continuous, whilst on Hilbert space it is discrete. Put in other words, this difference goes along the way followed for a long time, it refers to the different nature of elementary particles. Answer of this type completely obscure the probabilistic side of the question. We are able to give in fully probability terms a deduction of the equilibrium probability distribution for the elements of a finite abstract system. Specializing this distribution we reach equilibrium distributions for classical particles, bosons and fermions. Moreover we are able to deduce Gentile's parastatistics too.