Lesson 8 of 14 · All lessons in this module
  1. Random variables: PMF, PDF and CDF
  2. Expected value, variance and standard deviationVideo lesson
  3. Variance and covariance shortcuts, and the law of large numbers
  4. Discrete distributions: uniform, binomial and Poisson
  5. Continuous uniform and normal distributions, and simulating random draws
  6. Log-normal and logistic distributions, and the moments of key distributions
  7. Integrated cases: reading probabilities and moments from a return model
  8. Conditional probability and probability trees
  9. Conditional expected values and variancesVideo lesson
  10. Covariance from a joint probability function
  11. Joint, marginal and conditional distributions as information arrives
  12. Bayes' formula: updating a probability with new informationVideo lesson
  13. Bayes in practice: diffuse priors, missing inputs and screening tests
  14. Integrated cases: a tree with model forecasts and a Bayes update

This lesson is part of the 2027 curriculum. You are following the 2026 curriculum, where it is not taught in this form. Switch if you are sitting the exam under the 2027 curriculum.

Lesson 8 of 14 · 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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