Enter the probability of event B given event A has occurred, the prior probability of A, and the prior probability of B into the calculator to determine the Bayesian probability. This calculator can also evaluate any of the variables given the others are known.

## Bayesian Probability Formula

The following formula is used to calculate the Bayesian probability.

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

Variables:

- P(A|B) is the probability of event A given event B has occurred P(B|A) is the probability of event B given event A has occurred P(A) is the prior probability or marginal probability of A P(B) is the prior or marginal probability of B

To calculate the Bayesian probability, multiply the probability of event B given event A has occurred by the prior probability of A. Then, divide this result by the prior probability of B. This gives the probability of event A given that event B has occurred, according to Bayes’ theorem.

## What is a Bayesian Probability?

Bayesian probability is a theory in statistics that provides a mathematical framework for updating probabilities based on new evidence. Named after Thomas Bayes, it interprets probability as a measure of belief or confidence in an event occurring, which can be updated as new data or information becomes available. This approach contrasts with classical or frequentist probability, which interprets probability as the long-run frequency of events. Bayesian probability is widely used in machine learning, data analysis, and statistical inference.

## How to Calculate Bayesian Probability?

The following steps outline how to calculate Bayesian Probability using the given formula:

- First, determine the probability of event B given event A has occurred (P(B|A)).
- Next, determine the prior probability or marginal probability of event A (P(A)).
- Next, determine the prior probability or marginal probability of event B (P(B)).
- Next, multiply the probability of event B given event A has occurred (P(B|A)) with the prior probability or marginal probability of event A (P(A)).
- Finally, divide the result by the prior probability or marginal probability of event B (P(B)).

**Example Problem:**

Use the following variables as an example problem to test your knowledge:

P(A|B): probability of event A given event B has occurred

P(B|A): probability of event B given event A has occurred

P(A): prior probability or marginal probability of A

P(B): prior or marginal probability of B