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Math Help - A and B independent - Not A and Not B also?

  1. #1
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    A and B independent - Not A and Not B also?

    Hello,

    If we know A and B are independent, could I ask how to show Not A and Not B are independent?
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  2. #2
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    This should follow directly from the definition of independent events. Where are u stuck?
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  3. #3
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    Quote Originally Posted by sharpe View Post
    Hello,

    If we know A and B are independent, could I ask how to show Not A and Not B are independent?
    if A and B are independent, P(A n B)=P(A) x P(B)

    P(A' n B')= P(A u B)'

    =1-(P(A u B))

    =1-[P(A)+P(B)-P(A) x p(B)]

    =1-P(A) x P(B')-P(B)

    =P(B')-P(A) x P(B')

    =P(A') x P(B')
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  4. #4
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    great thanks that is helpful
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