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- #1
- Jan 26, 2012
- 995
Thanks to those who participated in last week's POTW!! Here's this week's problem (and the last University POTW of 2012)!
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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:
Remember to read the POTW submission guidelines to find out how to submit your answers!
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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 $P(A\cap B) = P(A)P(B\mid A)$.
Remember to read the POTW submission guidelines to find out how to submit your answers!