Classical and quantum probability in the ε-model

We describe the probabilistic study of a hidden variable model in which the origin of the quantum probability is due to fluctuations of the internal state of the measuring apparatus. By varying the intensity of these fluctuations from zero to a maximal value, we describe in a heuristic manner the transition from classical behavior to quantum behavior. We characterize this transition in terms of the Accardi-Fedullo inequalities. This is a review article in which we gather our recent contributions to the subject, most of which have not been published in article form.