Conditional Probability Tree Diagrams
How to use tree diagrams for conditional probability and Bayes interview questions with priors, likelihoods, joint probabilities, and posteriors.
Candidates who need cleaner setup for sequential probability information.
Build branches in order
A tree diagram starts with the first uncertainty, then branches for later signals or outcomes. Each branch probability should be conditional on the path above it.
Multiply along paths
The probability of a full path is the product of branch probabilities along that path. These path probabilities are joint probabilities, which can then be added or normalized.
Normalize for posteriors
For Bayes questions, keep the paths matching the observed signal and normalize among them. This turns likelihoods and priors into the posterior probability.
Concrete example
For a hidden biased coin, branch first by which coin was chosen, then by the observed flips under each coin. The posterior for a coin is its matching path probability divided by all matching path probabilities.
When trees are useful
Trees are useful for sequential information, hidden states, and Bayes updates. They are less useful when a direct counting model or complement is clearly shorter.
Common mistakes
Candidates often put posterior probabilities directly on branches before computing them. Branches should represent known priors or likelihoods; posterior comes after normalization.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.