The rule that the probability P(E_i A ) of some event E_i , given that another event A has been observed, is P(E_i )P(A E_i )/P(A ), where P(E_i ) is the prior probability of E_i , determined either objectively or subjectively, and P(A ), the probability of A, is given by the sum over all possible events E_j of the quantity P(E_j )P(A E_j ).