Probability Tree

Mathematical Principles & Theorems

Models sequential stochastic processes via rooted probability tree diagrams. Product rule along branches yields joint path probability \(P(A \cap B) = P(A) \cdot P(B|A)\). The Law of Total Probability computes unconditional probability: \(P(B) = \sum_{i} P(A_i)P(B|A_i)\). Bayes' Theorem updates prior probabilities with experimental evidence: \(P(A_k|B) = \frac{P(A_k)P(B|A_k)}{\sum_i P(A_i)P(B|A_i)}\).

Operating Instructions

• Configure root event prior probabilities \(P(A)\) and conditional branch probabilities \(P(B|A)\).
• Click Build Tree to generate the interactive multi-stage probability branching diagram.
• Inspect terminal branch nodes showing exact joint probabilities \(P(A_i \cap B_j)\).
• Review the calculated Bayesian posterior probability table for inverted conditional queries.