how to prove this

**pengchao1024** · October 25th 2009, 02:18 PM

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

i try to set: $C=A\cap B, \ \ p_{C}=1$
but unsure if thats right.

**matheagle** · October 25th 2009, 02:39 PM

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

Thread: how to prove this

LinkBack

Thread Tools

Display

how to prove this

Similar Math Help Forum Discussions

Prove a/b and a/c then a/ (3b-7c)

prove,,,

Prove |w + z| <= |w| +|z|

prove that if sequence (an) converges, use def of limit of sequence to prove...

How to prove that n^2 + n + 2 is even??

Search Tags