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An examination is made of the differing implications from applying the twomainstream interpretations of probability, frequentist and Bayesian, to QM(quantum mechanics) theory for the Bohm-EPR experiment. The joint probabilitydistribution for the possible spin outcomes for two particles with coupledspins is examined. Contrasting conclusions are made: (i) Under the frequentistinterpretation, the QM spin distribution implies a widely-discussednon-locality because probabilistic conditioning on a spin measurement is viewedas corresponding to a causal influence. Under the Bayesian interpretation, thisconditioning is viewed as providing information relevant to the spinprobabilities and the argument for non-locality loses its force. (ii) Thefrequentist interpretation leads to the locality condition used by John Bell in1964 to establish conditions for the existence of hidden variables behind thespin probability distribution but this condition is not consistent with theproduct (Bayes) rule of probability theory. Under the Bayesian interpretation,there is no motivation for this locality condition and a new stochastichidden-variable model is given that reproduces the spin distribution. (iii)Bell's original 1964 inequality provides a necessary condition for theexistence of a third-order joint probability distribution for three spinvariables that is compatible through marginalization with the second-orderjoint distributions for the three possible spin pairs. Bell's inequality islogically equivalent to the 1969 CHSH inequality that involves expectations offour pairs of four spin variables; the CHSH inequality must be satisfied inorder for a fourth-order joint probability distribution for the four spinvariables to exist. When any of these inequalities are violated, a jointprobability distribution for three spin outcomes fails to be valid because someprobabilities are negative.

Contrasting Implications of the Frequentist and Bayesian Interpretations of Probability when Applied to Quantum Mechanics Theory