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Formula verified · Deterministic calculation

Bayes Theorem Calculator

Enter the prior probability, evidence likelihood given the hypothesis, and evidence likelihood given the alternative.

Posterior probability0.666666666667
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Result methodology

Deterministic calculation using the displayed formula and supplied inputs.

Solution steps
  1. P(H∩E) = 0.16000000000000003
  2. P(E) = 0.24000000000000005
  3. P(H|E) = 0.6666666666666666

How this calculator works

Bayes' theorem updates P(H) using P(E|H) and P(E|not H).

Formula

P(H|E)=P(E|H)P(H)/[P(E|H)P(H)+P(E|¬H)P(¬H)]

Updates a hypothesis probability using evidence and its likelihood under the alternative.

Worked example

Bayes posterior is a verified test case used by the calculation engine.

Assumptions and limitations

  • All supplied probabilities are between 0 and 1.
  • The alternative is the complement of the hypothesis.
  • Evidence probability must be non-zero.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint.

  • CalcuMint deterministic statistics engine

Frequently asked questions

What does the posterior represent?

It is the updated probability of the hypothesis after accounting for the supplied evidence.

What happens when evidence has zero probability?

The posterior is undefined, and the calculator rejects that case.

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