Bayes' Theorem Calculator
Easily calculate probabilities using Bayes' Theorem. Our online calculator helps you find posterior probability given prior, likelihood, and evidence. Perfect for statistics and probability calculations.
Enter Probabilities
Bayes' Theorem helps update the probability of a hypothesis based on new evidence. Input the probabilities below to calculate the posterior probability.
Probability of hypothesis before evidence.
Probability of evidence given hypothesis is true.
Overall probability of evidence.
Probability of hypothesis after considering evidence.
Result Visualization
The posterior probability, P(H|E), calculated using Bayes' Theorem is:
Bayes' Theorem Formula:
P(H|E) = Posterior Probability, P(E|H) = Likelihood, P(H) = Prior Probability, P(E) = Evidence Probability
P(H) (Prior) = , P(E|H) (Likelihood) = , P(E) (Evidence) =
Understanding Bayes' Theorem
Bayes' Theorem is a fundamental concept in probability theory and statistics that describes how to update the probability of a hypothesis based on new evidence. It's widely used in various fields, from medical diagnosis to machine learning.
- Prior Probability (P(H)): Your initial belief in the hypothesis before observing any evidence.
- Likelihood (P(E|H)): The probability of observing the evidence if the hypothesis is true.
- Evidence Probability (P(E)): The overall probability of observing the evidence.
- Posterior Probability (P(H|E)): Your updated belief in the hypothesis after considering the evidence. This is what Bayes' Theorem calculates.
In essence, Bayes' Theorem allows us to refine our understanding of the likelihood of an event by incorporating new data. It's a powerful tool for making informed decisions under uncertainty. For further reading, you can explore resources like Wikipedia on Bayes' Theorem or educational materials from statistics textbooks.