Pretest probability is often said that probability, posterior probability is a conditional probability, conditional probability but not necessarily posterior probability. Bayesian formula is the formula required by the pretest probability posterior probabilities.
As a simple example: a red ball pocket has three, two white balls, touch taken without replacement, requirements:
probability ⑴ red ball first touch (referred to as A),;
⑵ second touch the probability red ball (referred to as B),;
⑶ known second red ball touched, the first touch is seeking probability red ball.
Solution: ⑴ P (A) = 3 /5, which is pretest probability;
⑵ P (B) = P (A) P (B | A) + P (A Inverse) P (B | A reverse) = (3 /. 5) × (1/2) + (2/5) × (3/4) = of 3/5
⑶ P (A | B) = P (A) P (B | A) / P (B) = ( 3/5) × (1/2) / ( 3/5) = 1/2, which is the posterior probability.