In probability theory, Bayes' theorem also called Bayes' law after Rev Thomas Bayes compares the conditional and marginal probabilities of two random events. It is often used to calculate posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to calculate the likelihood that a proposed analysis is accurate, given that observation. 
As an official theorem, Bayes' theorem is valid in all universal interpretations of probability. However, it plays a fundamental role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications.
 Frequentists assign probabilities to random events according to their frequencies of happening or to subsets of populations as proportions of the whole. Whilst Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates in greater detail.
Bayes' theorem compares the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability.
Each term in Bayes' theorem has a conventional name:
P(A) is the previous probability  of A. It is "previous" in the sense that it does not take into account any information about B.
P(A|B) is the conditional probability of A, given B. It is also called the subsequent probability because it is derived from or depends upon the specified value of B.
P(B|A) is the conditional probability of B given A.
P(B) is the previous.