

Subject:
Probability
Category: Science > Math Asked by: mms03ga List Price: $4.00 
Posted:
08 Dec 2002 18:36 PST
Expires: 07 Jan 2003 18:36 PST Question ID: 121595 
If M and N are independent events, P(M,N) = P(M)P(N) then prove that M' and N' are independent.  
 
 
 
 


Subject:
Re: Probability
Answered By: dannidinga on 09 Dec 2002 01:05 PST Rated: 
This is a repost of the answer I wrote as a request for clarification: M and N are independent, therefore P(M,N) = P(M)P(N)  this is simply the definition of independent events. Now let us prove that P(M',N')=P(M')P(N'), and therefore M' and N' are independent: I denote the union of two events A and B by AuB, and their intersection by (A,B). P(M',N') = P((MuN)') = 1  P(MuN) = 1  P(M u (N,M')) = = 1  (P(M) + P(N,M')) = 1  P(M)  P(N,M') = = 1  P(M)  (P(N)  P(N,M)) = = 1  P(M)  P(N) + P(N,M) = = 1  P(M)  P(N) + P(M)P(N) = = (1  P(M))(1  P(N)) = = P(M')P(N') 
mms03ga
rated this answer:
and gave an additional tip of:
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Awesome answer. It was very easy to understand the answer to the problem, with all the steps shown accurately. 

Subject:
Re: Probability
From: hailstormga on 08 Dec 2002 20:37 PST 
Isn't this impossible for the case of M' = N'? 
Subject:
Re: Probability
From: mms03ga on 08 Dec 2002 22:03 PST 
I dont see how M' will ever equal N' If M and N are independent events, we should be able to prove that M' and N' are also independent. 
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