Theorem 3.12. For n events A1, A2, An, we have ••.. P(A1NA20... O An) = P (A¡) P(A2\A¡) P(A3\A1 n A2)... xP(A,I A¡ N An..n An -1) .. where P(A;| A¡n Ak n...n A) represents the conditional probability...

Prove the theorem

Extracted text: Theorem 3.12. For n events A1, A2, An, we have ••.. P(A1NA20... O An) = P (A¡) P(A2\A¡) P(A3\A1 n A2)... xP(A,I A¡ N An..n An -1) .. where P(A;| A¡n Ak n...n A) represents the conditional probability of the event A; given that the events A¡, Ak A¡ have already happened. ••..