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Math Help - proof of independent probability

  1. #1
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    proof of independent probability

    How can i prove that if 2 events are independent then the probability

    P(AnB) = P(A)P(B)????
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  2. #2
    Super Member Random Variable's Avatar
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     P (A \cap B) = P(A|B)P(B) = P(A)P(B)
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  3. #3
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    lol ok without using the P(A/B)????

    Please prove it WITHOUT the fact the P(A/B) = P(AnB)/P(B)
    Last edited by mr fantastic; April 5th 2010 at 02:50 PM. Reason: Merged posts
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by millwallcrazy View Post
    How can i prove that if 2 events are independent then the probability

    P(AnB) = P(A)P(B)????
    What definition of independence are you using? The above is the definition I would normally use.

    CB
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  5. #5
    MHF Contributor matheagle's Avatar
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    The three equivalent definitions of independence are

    P(AB)=P(A)P(B)
    P(A|B)=P(A)
    P(B|A)=P(B)

    If any one holds the other two hold, if any one fails...
    You can also throw in
    P(A'|B)=P(A')
    P(A|B')=P(A)..................
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