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Math Help - Proof using Boole's Inequaility

  1. #1
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    Proof using Boole's Inequaility

    Let A_1, A_2, A_3, ... be a sequence of events of an experiment. Prove that P(\displaystyle\cap_{n=1}^{\infty} A_n) \geq 1 - \displaystyle\sum_{n=1}^{\infty} P( A_n)

    Hint: Use Boole's Inequality
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  2. #2
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Zennie View Post
    Let A_1, A_2, A_3, ... be a sequence of events of an experiment. Prove that P(\displaystyle\cap_{n=1}^{\infty} A_n) \geq 1 - \displaystyle\sum_{n=1}^{\infty} P( A_n)

    Hint: Use Boole's Inequality
    I'd use P(\cup_{n=1}^{\infty} A_n) \leq \sum_{n=1}^{\infty} P( A_n)

    and then the complement.
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