A posteriori probability

of an event

The conditional probability of an event taking place under certain conditions, to be contrasted with its unconditional or a priori probability. There is no difference between the meaning of the terms "conditional" and "a posteriori". The former term is employed if the condition itself is hypothetical and is not directly observed in the course of the experiment. The latter term is employed if it is desired to stress that the condition in question is actually observed. The a posteriori probability is connected with the a priori probability by the Bayes formula.