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Thread: Total probability formula on conditional probability

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    Total probability formula on conditional probability




    Hi,

    i'm studying one mathematical model for game theory and there is a formula that i'm not sure it is correct. It says:

    p(z/Y)=p(z,cs/Y) + p(z,ds/Y)

    where:
    p(z/Y), probability to occur event z for a given event Y.
    cs and ds are mutually exclusive events.

    Is this formula correct?

    According to the total probability theorem:

    P(z) = P(z,cs) + P(z,ds) = P(z/cs)*p(cs)+p(z/ds)*p(ds),
    but i'm not sure that this formula can be applied for p(z/Y) as it is done above?!

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    Re: Total probability formula on conditional probability


    Yes that is correct.

    Basically conditional probability is nothing but just another probability (measure), so all properties/facts/theorem ... of ordinary probability can also be applied to conditional probability.

    So you can just view this conditional probability like

    Q(\cdot) = P(\cdot|Y)

    And one reminder: In the law of total probability, not only the events are required to be mutually exclusive, but collectively exhaustive as well.

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