Why God might play dice

We study the question of the existence of hidden variables within the formalism of Pitowsky. We show that probabilities admit factorizable hidden variable models iff they admit a Kolmogorovian representation. In particular, directly deduced experimental frequencies always admit a factorizable hidden variable model and thus a Kolmogorovian representation. We apply this result in the framework of Bell's inequalities. We show that a deterministic interpretation of the hidden variables associated with this situation refutes the possibility for the experimenter of choosing freely the conditions of experimentation.