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Thread: de Morgan's law

  1. #1
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    de Morgan's law




    I need help. I just can't figure out where to go with this one..

    For two events A and B show that:

    P(A intersection B) is greater than or equal to P(A) + P(B) - 1

    Hint: Apply de Morgan's law and then the Bonferroni inequality.

    (I don't know how to type the symbols out, so I used words instead)

    Help is greatly appreciated... Extra 'bubbly' all around..

  2. #2
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    Hi
    The De Morgan's law is:P(AUB) = P(A) + P(B) - P(A intersection B)

    And we know that P(AUB) <= 1

    Implies: P(AUB) = P(A) + P(B) - P(A intersection B) <= 1
    Implies: P(A) + P(B) - P(A intersection B) <= 1
    Implies: P(A) + P(B) - P(A intersection B) - 1 <= 1 - 1
    Implies: P(A) + P(B) - P(A intersection B) - 1 <= 0
    Implies: P(A) + P(B) - 1 <= P(A intersection B)
    Thus,
    P(A intersection B) >= P(A) + P(B) - 1.

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