Bayes’ Theorem states that the conditional probability of an event, based on the occurrence of another event, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event.

**What Is Calculated in Bayes’ Theorem?**

Bayes’ Theorem calculates the conditional probability of an event, based on the values of specific related known probabilities.

**What Is a Bayes’ Theorem Calculator?**

A Bayes’ Theorem Calculator figures the probability of an event **A** conditional on another event **B**, given the prior probabilities of **A** and **B**, and the probability of **B** conditional on **A**. It calculates conditional probabilities based on known probabilities.

**How Is Bayes’ Theorem Used in Machine Learning?**

Bayes Theorem provides a useful method for thinking about the relationship between a data set and a probability. In other words, the theorem says that the probability of a given hypothesis being true based on specific observed data can be stated as finding the probability of observing the data given the hypothesis multiplied by the probability of the hypothesis being true regardless of the data, divided by the probability of observing the data regardless of the hypothesis.

**The Bottom Line**

At its simplest, Bayes’ Theorem takes a test result and relates it to the conditional probability of that test result given other related events. For high probability false positives, the Theorem gives a more reasoned likelihood of a particular outcome.

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

Where:

- P(A|B) – the probability of event A occurring, given event B has occurred
- P(B|A) – the probability of event B occurring, given event A has occurred
- P(A) – the probability of event A
- P(B) – the probability of event B