how to prove this

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October 25th 2009, 02:18 PM
pengchao1024

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.
October 25th 2009, 02:39 PM
matheagle

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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