Probability Tree / Decision Tree
Updated 2026-08-13
INTRODUCTION
English translation pending.
CORE DEFINITION
A probability tree represents a sequence of decisions and chance events as nodes and branches, with a probability attached to each branch and each root-to-leaf path representing one possible sequence. The core proposition is that the probability of a compound event is the product of the branch probabilities along its path, which turns a confusing multi-stage problem into arithmetic on a diagram. The key qualification is that branch probabilities must be conditional on the path already taken, and the branches from any node must sum to one.
SCAFFOLDING EFFECT
Reduce cognitive load
- Node map: draw each decision point and chance event as a separate node in order. - Path product: multiply the branch probabilities along each path to get that sequence's probability. - Sum target: add the paths that satisfy your condition to get its total probability.
Anchor fast decisions
Multiplying along a path follows directly from the definition of conditional probability, since each branch states the chance of the next event given everything before it. The tree makes the conditioning visible, so it is harder to mistakenly use a marginal probability where a conditional one belongs. Enumerating paths also reveals sequences that intuition tends to overlook.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Decision_treeverified
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