# Bayes' theorem

Bayes' theorem, also known as **Bayes' rule**, is a result in probability
theory, named after Thomas Bayes, who proved
a special case of it. It is used in statistical inference to update estimates
of the probability that different hypotheses are true, based on observations
and a knowledge of how likely those observations are, given each hypothesis.
In fact, it is habitually used by scientists in preference to the principle
of induction. Bayes's theorem says that if an instance *X* is actually
observed, then the probability of a hypothesis *H* must be multiplied
by the following ratio:

probability of observing X if H is true |

probability of observing X |

In other words, the probability of a hypothesis *H* conditional on
a given body of data *X* is equal the ratio of the unconditional
probability of the conjunction of the hypothesis with the data to the unconditional
probability of the data alone.