"Violating'' Clauser-Horne inequalities within classical mechanics

Some authors have raised the question whether the probabilities stemming from a quantum mechanical computation are entitled to enter the Bell and the Clauser-Horne inequalities. They have remarked that if the quantum probabilities are given the status of conditional ones and the statistics for the various settings of the detectors in a given experiment is properly kept into account, the inequalities happen to be no longer violated. In the present paper a classical simile modeled after the quantum mechanical instances is closely scrutinised. It is shown that the neglect of the conditional character
of the probabilities in the classical model leads not only to “violate” the Clauser-Horne inequalities, but also to contradict the very axioms of classical probability theory.