Show that if the conditional probabilities exist, then

Chapter , Problem 45

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Show that if the conditional probabilities exist, then

\(P\left(A_{1} \cap A_{2} \cap \cdots \cap A_{n}\right) =P\left(A_{1}\right) P\left(A_{2} \mid A_{1}\right) P\left(A_{3} \mid A_{1} \cap A_{2}\right) \cdots P\left(A_{n} \mid A_{1} \cap A_{2} \cap \cdots \cap A_{n-1}\right)\)

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