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Subject: "Probability Question"     Previous Topic | Next Topic
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cleodsc
guest
Oct-21-05, 06:41 AM (EST)
 
"Probability Question"
 
   Ok I have an issue I need to prove the following (in notation): P(A)+P(B)-2P(AB)= (Ac U B) U (Bc U A)

I know how to prove this using real numbers, for instance knowing P(A)= .5 and P(B)=. 2 and (AB)= .1 which is .5+.2-2(.1)= .5, but I have no idea how to write this using notation. Any ideas?


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alexbadmin
Charter Member
1669 posts
Oct-21-05, 06:56 AM (EST)
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1. "RE: Probability Question"
In response to message #0
 
   >Ok I have an issue I need to prove the following (in
>notation): P(A)+P(B)-2P(AB)= (Ac U B) U (Bc U A)

You probably mean

A U B - AB = (Ac B) U (ABc), or

P(A U B) - 2P(AB) = P(Ac B) + P(ABc).

Venn diagrams are a useful tool that help visualize the situation here.

https://www.cut-the-knot.com/LewisCarroll/VennClick.shtml

You can use, say,

Ac B = B - A = B - AB.

Also,

(B-AB)(AB) = empty and (B - AB) U AB = B.

So that

P(Ac B) = P(B) - P(AB).

Similarly,

P(ABc) = P(A) - P(AB).


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