# Bayes' Theorem

## What is Bayes' Theorem?

Bayes' theorem is a mathematical theorem that is used to update the probability of an event occurring, given new evidence or information. It is named after Thomas Bayes, an 18th-century English statistician, and theologian who first developed the concept.

The theorem is expressed as follows:

P(A|B) = [P(B|A) * P(A)] / P(B)

Where:

P(A|B) is the probability of event A occurring, given that event B has occurred. P(B|A) is the probability of event B occurring, given that event A has occurred. P(A) is the probability of event A occurring. P(B) is the probability of event B occurring.

Bayes' theorem allows us to update the probability of an event occurring based on new evidence or information. For example, suppose we want to know the probability that a person has a certain medical condition, given that they have a certain symptom. We can use Bayes' theorem to update the probability of the person having the condition based on the probability of the symptom occurring in people with and without the condition.

Bayes' theorem is widely used in many fields, including statistics, machine learning, and artificial intelligence, to update probabilities and make decisions based on uncertain or incomplete information.