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Math Help - how to prove this

  1. #1
    Junior Member
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    how to prove this

    given \ \ \ \  P(A\cap B\cap C)= p_{A}p_{B}p_{C} ,\ \ \  prove :\ \ \  P(A\cap B)=p_{A}p_{B}


    i try to set:  C=A\cap B, \ \ p_{C}=1
    but unsure if thats right.
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  2. #2
    MHF Contributor matheagle's Avatar
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    Try AB=ABC\cup ABC'

    I assume you have independence between A, B and C, which implies independence between A, B and C'.

    So P(ABC)=P(A)P(B)P(C) and P(ABC')=P(A)P(B)P(C')

    add these....  P(A)P(B)P(C)+P(A)P(B)P(C')=P(A)P(B)\bigl[P(C)+P(C')\bigr]=P(AB)
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