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Check each split within its conditioning state
A fictional model has a strong state with probability 65% and a weak state with probability 35%. Revenue beats forecast with conditional probability 70% in the strong state and 25% in the weak state. Each complementary no-beat branch therefore has probability 30% or 75% within its own state.
Multiply the weights along each path
| Path | Product | Joint probability |
|---|---|---|
| Strong and beat | 65%×70% | 45.5% |
| Strong and no beat | 65%×30% | 19.5% |
| Weak and beat | 35%×25% | 8.75% |
| Weak and no beat | 35%×75% | 26.25% |
| All terminal paths | 100% |
Recover the first-stage probabilities
The two strong-state paths sum to 65%, and the two weak-state paths sum to 35%. Adding the two beat paths gives 54.25%. These checks compare terminal assignments with both the root and conditional inputs.
Recognise a terminal total that hides an error
Assigning 65% to strong-and-beat, 35% to weak-and-beat and zero to the other two paths would also sum to one. It would contradict the supplied conditional beat probabilities. A total of one alone therefore cannot confirm the tree was constructed correctly.