Probability as a Theory Dependent Concept

It is argued that probability should be deened implicitly by the distributions of possible measurement values characteristic of a theory. These distributions are tested by, but not deened in terms of, relative frequencies of occurrences of events of a speciied kind. The adoption of an a priori probability in an empirical investigation constitutes part of the formulation of a theory. In particular, an assumption of equiprobability in a given situation is merely one hypothesis inter alia, w h i c h can be tested, like a n y other assumption. Probability in relation to some theories | for example quantum mechanics | need not satisfy the Kolmogorov axioms. To illustrate how two theories about the same system can generate quite different probabilistic predictions, a team game for three players is described. If only classical methods are allowed, a 75% success rate at bestcan be achieved in repeated trials. Nevertheless, a quantum strategy exists that gives a 100% probability of winning.