"Violating" Clauser-Horne inequalities within classical mechanics

Some authors have raised the question whether the probabilities stemming fr om a quantum-mechanical computation are entitled to enter the Bell and the Clauser-Horne inequalities. They have remarked that if the quantum probabil ities are given the status of conditional ones and the statistics for the v arious settings of the detectors in a given experiment is properly kept int o 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 chara cter of the probabilites in the classical model leads not only to "violate" the Clauser-Horne inequalities, but also to contradict the very axioms of classical probability theory.