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Math Help - Complement Proof of independent events

  1. #1
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    Complement Proof of independent events

    If A and B are independent events, show that \bar{A} \ \ \text{and} \ \ \bar{B} are independent.

    I haven't a clue what to do for this one.
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by dwsmith View Post
    If A and B are independent events, show that \bar{A} \ \ \text{and} \ \ \bar{B} are independent.

    I haven't a clue what to do for this one.
    I usually write A^c for complements. You can show P(A^c \cap B^c) = P(A^c) P(B^c).


    P(A^c \cap B^c)

    = P[(A \cup B)^c]

    = 1-P(A \cup B)

    = 1-P(A)-P(B)+P(A\cap B)

    now use P(A\cap B) = P(A) P(B)\; and\; P(A^c)=1-P(A)\;and\;P(B^c)=1-P(B) and simplify
    Last edited by harish21; February 3rd 2011 at 06:22 PM.
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