Bell's inequality in terms of probabilities

Bell’s inequality is a reality test that can be applied to the results of experiments. If the experimental results satisfy the inequality, then the experiment has an underlying reality that obeys the classical laws. If the results violate the inequality, then the experiment is incompatible with classical theory and there is no process that can replicate the quantum results. We first obtain a form of Bell’s inequality in terms of probabilities by analyzing the results of a true-false exam. The inequality is obtained by simply comparing answer sheets. This straightforward approach contains no physics, but we tacitly assume that Separability and Locality, pillars of classical theory, are in effect. We then analyze the EPR experiment by calculating the quantum probabilities for Alice and Bob separately and then comparing their results. This approach satisfies the Bell inequality, but the quantum probability with Alice and Bob entangled into a whole entity violates it. We conclude, as did Bell, that we cannot avoid the non-locality inherent in quantum mechanics.