Bayes Theorem Calculator

Calculate conditional probability using Bayes' Theorem. Input prior probability, likelihood, and evidence to find posterior probability.

Calculator

(0-1)

Your initial belief about the probability of event A

(0-1)

Probability of observing evidence B given that A is true

(0-1)

Total probability of observing evidence B

Results

Enter values and click Calculate to see results

About Bayes' Theorem

Bayes' Theorem is a fundamental concept in probability theory that describes how to update the probability of a hypothesis based on new evidence.

Formula:

P(A|B) = [P(A) × P(B|A)] ÷ P(B)

Where:

  • P(A|B) is the posterior probability - the probability of event A occurring given that event B has occurred
  • P(A) is the prior probability - your initial belief about the probability of event A
  • P(B|A) is the likelihood - the probability of observing evidence B given that A is true
  • P(B) is the evidence - the total probability of observing evidence B

Applications:

  • Medical diagnosis and testing
  • Machine learning and artificial intelligence
  • Risk assessment and decision making
  • Statistical inference
  • Quality control and reliability analysis