Bayesian Probability

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Calculate the probability of an event based on prior knowledge and new evidence.

Probability Parameters

Prior Probability P(A)

Likelihood P(B|A)

Likelihood P(B|¬A)

Calculation Results

16.67%

Posterior P(A|B)

The updated probability of A given the evidence B has occurred.

Probability P(B)5.94%

Updated Belief

P(A|B)16.7%

About this calculator

What is Bayesian Inference?

Bayesian probability is an interpretation of the concept of probability where probability is treated as a degree of belief in a proposition. Bayes' theorem describes how to update this belief when new evidence is encountered. It is the core of modern machine learning, medical diagnosis, and scientific forecasting.

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Pro Tips

P(A) is your initial belief (Prior).
P(B|A) is how likely the evidence is if your belief is true.
P(B|¬A) is how likely the evidence is if your belief is false (False Positive).

Fun Facts

"Thomas Bayes, the developer of the theorem, was an 18th-century minister whose work on probability was published posthumously."
"Spam filters use Bayesian probability to identify junk email based on the presence of certain words like 'win' or 'free'."
"In medical testing, even a test with 99% accuracy can have a high false-positive rate if the condition is extremely rare in the population."

Formula: P(A|B) = [P(B|A) × P(A)] / P(B)