Bayes Rule Calculator: Master Posterior Probability

Calculate Bayesian Probability Instantly

Enter a decimal between 0 and 1 representing the probability of event A.
Enter a decimal between 0 and 1 representing the probability of B given A has occurred.
Enter a decimal between 0 and 1 representing the probability of B given A has NOT occurred.

Calculation Results:

Posterior Probability P(A|B):

Marginal Probability P(B):

Probability P(~A):

Posterior Probability P(~A|B):

Our Bayes Rule Calculator simplifies complex conditional probability calculations. Easily compute posterior probabilities like P(A|B) by inputting prior probabilities and likelihoods. Perfect for students, data scientists, and anyone needing to apply Bayes' Theorem in real-world scenarios.

Formula:

P(A|B) = [P(B|A) * P(A)] / P(B)
P(B) = P(B|A) * P(A) + P(B|~A) * P(~A)
P(~A) = 1 - P(A)

Variables Explained:

  • P(A): Prior Probability of event A
  • P(B|A): Conditional Probability of event B given event A (Likelihood)
  • P(B|~A): Conditional Probability of event B given NOT event A (Likelihood for ~A)
  • P(A|B): Posterior Probability of event A given event B
  • P(B): Marginal Probability of event B
  • P(~A): Probability of NOT event A

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