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Math Help - Test the Pair of Events for Independence

  1. #1
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    Exclamation Test the Pair of Events for Independence

    A B C Total
    D 0.18 0.12 0.00 0.30
    E 0.42 0.28 0.00 0.70
    Totals 0.60 0.40 0.00 1.00

    Are the events C and E independent?

    I know the answer is no, not how are they not independent? I've been struggling a bit with probability and cannot seem to figure this out.
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  2. #2
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    Re: Test the Pair of Events for Independence

    Quote Originally Posted by michellederz View Post
    A B C Total
    D 0.18 0.12 0.00 0.30
    E 0.42 0.28 0.00 0.70
    Totals 0.60 0.40 0.00 1.00

    Are the events C and E independent?

    I know the answer is no, not how are they not independent? I've been struggling a bit with probability and cannot seem to figure this out.
    The usual check for the independence of two events E1 and E2 is that

    Pr[E1 AND E2] = Pr[E1] * Pr[E2]

    In this case

    Pr[E AND C] = 0

    Pr[E] = 0.7
    Pr[C] = 0

    0 = 0.7 * 0

    so

    Pr[E AND C] = Pr[E] * Pr[C] and so E and C are independent. I'm not sure how you know they aren't.
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