Bayes' rule, also known as Bayes' theorem or Bayes' law, is a mathematical formula used in probability theory and statistics to calculate the probability of an event based on prior knowledge or information. It is named after the Reverend Thomas Bayes, an 18th-century British statistician and theologian who developed the concept. Bayes' rule states that the probability of an event A given that event B has occurred is equal to the probability of event B given that event A has occurred, multiplied by the probability of event A occurring, divided by the probability of event B occurring. This can be expressed as:

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

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A occurring, and P(B) is the prior probability of event B occurring. Bayes' rule is widely used in fields such as machine learning, artificial intelligence, and data science to make predictions and decisions based on uncertain or incomplete information.