Update a prior probability using evidence likelihoods. Calculate posterior probability, total evidence probability and the likelihood ratio.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs. Probability inputs are percentages from 0 to 100, not decimal fractions.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
P(A | B) = P(A)P(B | A) / [P(A)P(B | A) + P(not A)P(B | not A)].
Assumptions and limits
Two exhaustive hypotheses and one observed event. Inputs must refer to the same population and evidence. Sequential updating requires appropriate conditional likelihoods, not automatic independence.
Worked example
With prior P(A) = 10%, evidence likelihood P(B | A) = 80% and P(B | not A) = 20%, the two evidence contributions are 0.08 and 0.18. Total evidence probability is 0.26. The posterior is 0.08/0.26 = 4/13, approximately 30.7692%. Reversing P(B | A) and P(A | B) would answer the wrong question. Both likelihoods and the prior must describe a compatible observation model.
Worked reading and practical questions
- Update a Supplier Defect Probability After an Inspection Flag
- Likelihood Ratios and Sequential Evidence: When Can You Multiply?
Browse Statistics calculators or explore other tools on the GreenCalc homepage.
Frequently asked questions
What does this calculator assume?
Two exhaustive hypotheses and one observed event. Inputs must refer to the same population and evidence. Sequential updating requires appropriate conditional likelihoods, not automatic independence.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.