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Math Help - prove occurrences are independently of each other

  1. #1
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    prove occurrences are independently of each other

    I have problems with this task, I couldnt join the lecture and now i dont get it so every help would be appreciated

    Throw two times a fair dice. Prove that these occurrences are pairwise independently of each other but not independently of each other.
    A = "number of the first cast of dice is even"
    B = "number of the second cast of dice is odd"
    C= " both numbers are either even or odd"

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  2. #2
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    Re: prove occurrences are independently of each other

    Quote Originally Posted by suslik View Post
    Throw two times a fair die. Prove that these occurrences are pairwise independently of each other but not independently of each other.
    A = "number of the first cast of die is even"
    B = "number of the second cast of die is odd"
    C= " both numbers are either even or odd"
    First, it is one die and two dice.
    The outcome space is
    \begin{array}{*{10}{c}}  E&E \\  E&O \\   O&E \\   O&O \end{array}
    You can see the \mathcal{P}(A)=\mathcal{P}(B)=0.5, two out of four for each event.

    BUT \mathcal{P}(AB)=0.25, an even then an odd.

    So \mathcal{P}(A)\cdot\mathcal{P}(B)=\mathcal{P}(AB) showing independence.
    Last edited by Plato; June 2nd 2012 at 04:38 AM.
    Thanks from suslik
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