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- Jan 26, 2012

- 995

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**Problem**: For events $E_1$, $E_2,\ldots,\,E_n$, justify the following probability identity: \[P(E_1\cap E_2\cap\cdots\cap E_n)=P(E_1)P(E_2\mid E_1)P(E_3\mid E_2\cap E_1)\cdots P(E_n\mid E_1\cap E_2\cap\cdots \cap E_{n-1}).\]

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**Hint**:

Use the fact that $P(A\cap B) = P(A)P(B\mid A)$.

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