Introduction to Probability · Problem 4.1.16

Conditional Probability — Grinstead & Snell

Mathematics — Probability · conditional-probability-chain-rule

Problem

Prove that for any three events

A

B

C

, each having positive probability, and with the property that

P(A \cap B) > 0

P(A \cap B \cap C) = P(A)P(B|A)P(C|A \cap B) .