Posterior probability is a revised probability that takes into account new available information. For example, let there be two urns, urn A having 5 black balls and 10 red balls and urn B having 10 black balls and 5 red balls. Now if an urn is selected at random, the probability that urn A is chosen is 0.5. This is the a priori probability. If we are given an additional piece of information that a ball was drawn at random from the selected urn, and that ball was black, what is the probability that the chosen urn is urn A? Posterior probability takes into account this additional information and revises the probability downward from 0.5 to 0.333 according to Bayes´ theorem, because a black ball is more probable from urn B than urn A.