Bayes’ theorem was names after Rev Thomas Bayes and is a method used
in probability theory. This theorem aims to relate the conditional and
marginal probabilities of two random events occuring, and given
various observations is frequently used to compute subsequent
probabilities. Bayes’ theorem is also often known as Bayes’ law.

An example of where Bayes’ theorem may be used is in the following
extract: “Suppose there exists a school with forty percent females and
sixty percent males as students. The female students can only wear
skirts or trousers in equal numbers whereas all the male students can
only wear trousers. An observer randomly sees a student from a
distance and all he can see is that this student is wearing
trousers. What is the probability this student is female?”

There is a debate amongst frequentists and Bayesians about how Bayes’
theorem plays a major role around the beginnings of statistical
mathematics. Frequentist and Bayesian explanations do not agree about
the ways in which probabilities should be assigned. This is primarily
because Bayesians assign probabilities in terms of beliefs whereas
frequentists assign probabilities to random events according to the
frequencies of them occurring.