what is a posterior probability 
a posterior probability in bayesian statistics is the revised or updated probability of an event occurring after taking into consideration new information the posterior probability is calculated by updating the prior probability using bayes theorem in statistical terms the posterior probability is the probability of event a occurring given that event b has occurred bayes theorem formulathe formula to calculate a posterior probability of a occurring given that b occurred p a b p a b p b p a p b a p b where a b events p b a the probability of b occurring given that a is true p a and p b the probabilities of a occurring and b occurring independently of each other begin aligned p a mid b frac p a cap b p b frac p a times p b mid a p b textbf where a b text events p b mid a text the probability of b occurring given that a text is true p a text and p b text the probabilities of a occurring text and b occurring independently of each other end aligned p a b p b p a b p b p a p b a where a b eventsp b a the probability of b occurring given that ais truep a and p b the probabilities of a occurringand b occurring independently of each other the posterior probability is thus the resulting distribution p a b 1