What is Bayes’ Theorem?

Bayes’ Theorem is a mathematical formula used in probability theory to determine the conditional probability of an event, given some prior knowledge or information. It was named after Reverend Thomas Bayes, an English statistician, and theologian.

Bayes’ Theorem 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 prior probability of event A, divided by the prior probability of event B. In mathematical notation, it 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 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. P(B) is the prior probability of event B.

Bayes’ Theorem is widely used in fields such as machine learning, data science, and artificial intelligence to make predictions and decisions based on available data and prior knowledge.