Grinstead-Snell-Probability · Problem 4.1.16

Conditional Probability

Mathematics · conditional-probability-product-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).