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Lesson 7 of 12 · 14 min

Conditional probability and probability trees

A probability tree splits an uncertain outcome into scenarios and then into outcomes conditional on each scenario, so joint and total probabilities can be read straight off its branches.

In short

  • A conditional probability P(A∣B)P(A \mid B) is the chance of A once you know B has happened: P(AB)/P(B)P(AB)/P(B).
  • The joint probability of two events is P(AB)=P(A∣B)P(B)P(AB) = P(A \mid B)P(B): on a tree, multiply along the branches.
  • First-level branches are scenarios that must be mutually exclusive and exhaustive; later branches are conditional on the branch they grow from.
  • The total probability rule writes an unconditional probability as the scenario-weighted sum of conditional probabilities.
  • All end-node probabilities sum to 1, a built-in check on your tree.

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Conditional probability and probability trees · Statistical Distributions for Financial Asset Prices and Returns