Follow each branch by multiplying conditional probabilities; add mutually exclusive terminal paths when the question combines them.
StartAP(A)not A1 − P(A)A and BA and not Bnot A and Bneither
1EnterProvide the known values
2CalculateResults update automatically
3VerifyReview the details and units
Try an example
Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.
Statistics result
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What the probability tree calculator is calculating
Following conditional branches. Conditional probability changes the reference group. A branch probability must be read inside the branch condition, while Bayes’ theorem reverses the conditioning direction using prior probabilities.
1Define exhaustive starting branches2Multiply along each path3Add relevant paths or normalize posteriors
Probability rule
Path probability multiplies along branches; a marginal probability adds its mutually exclusive complete paths.
Every probability must remain between 0 and 1, and overlapping regions must be jointly feasible. The calculator rejects combinations that violate the stated model.
How to interpret it
The four leaf paths partition the sample space and reveal exactly which first-stage branches contribute to the second event.
Model boundary: The tree models two exhaustive binary stages; entered conditional probabilities must refer to the same B event under A and not A.
Quick guide
How to use this calculator
Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the probability tree calculator works
Path probability multiplies along branches; a marginal probability adds its mutually exclusive complete paths.
The four leaf paths partition the sample space and reveal exactly which first-stage branches contribute to the second event.
Worked example
Probability Tree example
If P(A)=0.3, P(B|A)=0.8, and P(B|not A)=0.2, then P(B)=0.38.
Path probability multiplies along branches; a marginal probability adds its mutually exclusive complete paths.
Supported inputs
Precision and limits
Model and design
The tree models two exhaustive binary stages; entered conditional probabilities must refer to the same B event under A and not A.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
The four leaf paths partition the sample space and reveal exactly which first-stage branches contribute to the second event.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
