Probability
Decision Tree Probability Calculator
Combine two first-stage branches with branch-specific success rates, calculate a posterior branch probability, and evaluate a two-outcome expected value.
Probability of branch B-
Joint probability: A and success-
Joint probability: B and success-
Overall success probability-
Probability branch A given success-
Expected outcome value-
Decision view
Two-stage probability tree with joint leaf weights
Two-stage probability tree with joint leaf weightsBranch probabilities split first, conditional outcomes split second, and success leaves merge into the total event probability.
Exact scenario comparisonProbability of branch A (%) changes while all other entered assumptions remain constant.
| Probability of branch A (%) | Probability of branch B | Joint probability: A and success | Joint probability: B and success | Overall success probability | Probability branch A given success | Expected outcome value |
|---|
How to use Decision Tree Probability Calculator
- Define mutually exclusive first-stage branches.
- Enter success probability conditional on each branch.
- Keep outcome values separate from probabilities until the final expectation.
Calculator guide
Understanding Decision Tree Probability Calculator
A decision tree keeps conditional probabilities attached to the path where they apply. Multiplication moves along a path; addition combines mutually exclusive leaves.
Detailed calculation process
Detailed two-stage probability-tree calculation
The default tree sends 60% of cases to A and 40% to B, with conditional success rates of 75% and 40%.
General formula: P(A∩S)=P(A)P(S|A)P(B∩S)=P(B)P(S|B)P(S)=P(A∩S)+P(B∩S)P(A|S)=P(A∩S)/P(S)EV=P(S)V_S+[1-P(S)]V_F Each leaf is a joint path. Success leaves are mutually exclusive, so their probabilities add.
What each symbol means
Worked substitution with the default inputs
The default overall success probability is 61%, with expected value $25,820.
Worked situations
Practical examples
- Branch A contributes 60%×75%=45 percentage points of success.
- Branch B contributes 40%×40%=16 points, so overall success is 61%.
Better inputs
Useful tips
- Make branch probabilities exhaustive.
- Use conditional—not overall—rates on second-stage edges.
- Add more branches only when they change the decision.
Before relying on the result
Limitations and common mistakes
- Only two first-stage branches and two final outcomes are modeled.
- Probabilities are treated as known and values are undiscounted.
- Dependencies outside the stated conditional structure are absent.
Reference
Key terms
- Joint probability
- Probability that every event on one path occurs.
- Conditional probability
- Outcome probability given an earlier branch.
- Posterior
- Updated branch probability after observing success.
Important note
Audit branch completeness, conditional data, value timing, risk tolerance, and model uncertainty before using a probability tree for consequential decisions.
Frequently asked questions
Why is overall success not the simple average?
Conditional success rates are weighted by unequal branch probabilities.
What does P(A|success) mean?
Among successful outcomes, it is the share that traveled through branch A.
Can expected value be an impossible outcome?
Yes. It is a probability-weighted long-run average.