  The conventional postulate for the probabilistic interpretation of quantum
mechanics is asymmetric in preparation and measurement, making retrodiction
reliant on inference by use of Bayes' theorem. Here, a more fundamental
symmetric postulate is presented, from which both predictive and retrodictive
probabilities emerge immediately, even where measurement devices more general
than those usually considered are involved. It is shown that the new postulate
is perfectly consistent with the conventional postulate.
