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Thread: Quick probability proof

  1. September 15th 2010, 09:47 AM #1
    Zennie
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    Quick probability proof

    Let A and B be two events. Prove that P(AB) \geq P(A) + P(B) - 1
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  2. September 15th 2010, 09:51 AM #2
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    Quote Originally Posted by Zennie View Post
    Let A and B be two events. Prove that P(AB) \geq P(A) + P(B) - 1
    Assuming P(AB) means P(A\cup B), use that P(A\cup B) = P(A) + P(B) - P(A \cap B) and that 0\le P(X) \le1 for any event \,X.
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  3. September 15th 2010, 10:44 AM #3
    Zennie
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    Sorry for the lack of clarity.

    P(AB) means P(A \cap B). So prove that P(A \cap B) \geq P(A) + P(B) - 1
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  4. September 15th 2010, 10:50 AM #4
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    Quote Originally Posted by Zennie View Post
    Sorry for the lack of clarity.

    P(AB) means P(A \cap B). So prove that P(A \cap B) \geq P(A) + P(B) - 1
    If you solve for P(A \cap B) you'll see it works out the same.
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