Free · Probability and classification
Two-Event Probability Tree and Bayes Updates
Work through complementary event branches, joint outcomes and conditional updates in a two-event probability tree.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
In this example, event B1 has probability 40%, and P(A1 given B1) is 70%.
Joint probability = prior × conditional probability; posterior = joint probability / observed-event probability.
Worked example
Enter these known values and leave the other values blank.
- P(A)
- 0.4
- P(B | A)
- 0.7
- P(B | Ā)
- 0.2
- P(B̅ | A)
- 0.3
- P(A ∩ B)
- 0.28
- P(A ∩ B̅)
- 0.12
- P(Ā)
- 0.6
- P(B̅ | Ā)
- 0.8
- P(Ā ∩ B)
- 0.12
- P(Ā ∩ B̅)
- 0.48
- P(B)
- 0.4
- P(B̅)
- 0.6
- P(A | B)
- 0.7
- P(A | B̅)
- 0.2
- P(Ā | B)
- 0.3
- P(Ā | B̅)
- 0.8
Assumptions and limitations
- A1 and A2 are complementary events; B1 and B2 are complementary events. The four joint outcomes are mutually exclusive and exhaustive.
- Conditional probabilities need a positive conditioning-event probability. A posterior for an event of zero probability is undefined, so it remains incomplete.
- Dependence is allowed. Multiplication uses the conditional probability on its own prior branch rather than assuming independence.
Common questions
How are probabilities entered?
Enter decimals between zero and one. For example, 0.4 represents 40%.
Can I solve for a missing input?
Yes, where the relationship has a finite, determined inverse. Clear the unknown and lock known controls; singular cases can remain incomplete.
References
Bookify replaces the captured explanatory diagram with original accessible text preserving its probability or classification relationships.
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