In probability theory; Bayes theorem (often called Bayes law after Rev
Thomas Bayes) relates the conditional and marginal probabilities of
two random events. It is used to compute posterior probabilities given
observations. For example; a person may be observed to have certain
symptoms. Bayes theorem can be used to compute the probability that a
proposed diagnosis is correct.

As a formal theorem Bayes theorem is valid in all common
interpretations of probability. However, it plays a central role in
the debate around the foundations of statistics: frequentist and
Bayesian interpretations disagree about the ways in which
probabilities should be assigned to each other. Bayesians describe
probabilities in terms of beliefs and degrees of uncertainty, While
frequentists assign probabilities to random events according to their
frequencies of occurrence or to subsets of populations as proportions
of the whole. The articles on Bayesian probability and frequentist
probability discuss these debates in detail.