Violation of Bell quantum probability inequalities with classical fields

Violations of Bell inequalities in classical optics have been demonstrated in terms of field mean intensities and correlations, however, the quantum meaning of violations point to statistics and probabilities. We present a violation of Bell inequalities for classical fields in terms of probabilities, where we convert classical-field intensities into probabilities via the standard photon-counting equation. We find violation for both, entangled and separable field states. We conclude that any obtained quantum effect might be fully ascribed to the quantum nature of the detector rather than the field itself. Finally, we develop a new Bell-like criterion which is satisfied by factorized states and it is not by the entangled state.