For arbitrary events A, B and C with \(P(A\cap B)\gt 0\), which formula gives \(P(A\cap B\cap C)\)?
P (A) P(B|A) P(C|A ∩ B)
The multiplication rule gives \(P(A\cap B)=P(A)P(B\mid A)\). Therefore \(P(A\cap B\cap C)=P(A\cap B)P(C\mid A\cap B)=P(A)P(B\mid A)P(C\mid A\cap B)\). No independence assumption is needed; the stated positivity makes the conditional probabilities defined.
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