Enter the likelihood, prior probability, and evidence probability into the calculator to determine the posterior probability.

Posterior Probability Formula

The following formula is used to calculate the posterior probability.

P(H|E) = (P(E|H) * P(H)) / P(E)


  • P(H|E) is the posterior probability, the probability of hypothesis H given the evidence E.
  • P(E|H) is the likelihood, the probability of the evidence given that the hypothesis is true.
  • P(H) is the prior probability, the initial degree of belief in H.
  • P(E) is the evidence probability, the total probability of the evidence being observed.

To calculate the posterior probability, multiply the likelihood (the probability of the evidence given that the hypothesis is true) by the prior probability (the initial degree of belief in the hypothesis). Then, divide this product by the evidence probability (the total probability of the evidence being observed). This will give you the posterior probability, which is the revised or updated probability of the hypothesis given the observed evidence.

What is a Posterior Probability?

A posterior probability, in the context of Bayesian statistics, is the revised or updated probability of an event occurring after taking into consideration new information. It is calculated using Bayes’ theorem, which is a mathematical formula for determining conditional probability. The posterior probability helps to measure how the probability of a hypothesis changes when evidence is introduced. It is a fundamental concept in Bayesian inference, a statistical paradigm that answers research questions about unknown parameters using probability statements.

How to Calculate Posterior Probability?

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

  1. First, determine the likelihood (P(E|H)).
  2. Next, determine the prior probability (P(H)).
  3. Next, determine the evidence probability (P(E)).
  4. Next, multiply the likelihood (P(E|H)) by the prior probability (P(H)).
  5. Finally, divide the result by the evidence probability (P(E)) to calculate the posterior probability (P(H|E)).

Example Problem:

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

likelihood (P(E|H)) = 0.8

prior probability (P(H)) = 0.6

evidence probability (P(E)) = 0.5