Bayes' formula is an important method for computing conditional probabilities. It is often used to compute posterior probabilities (as opposed to priorior probabilities) given observations. For example, if a patient is observed to have a certain symptom, Bayes' formula can be used to compute the probability that a diagnosis is correct, given that observation. The so-called "prosecutor's fallacy" is a common fallacy of the statistical reasoning which can be very important in the comprehension of a positive result in any mass screening. It's at 8-th place in the list of "The Top Ten Statistical Errors" in Radiology.
