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 Subject: "Probability Question" Previous Topic | Next Topic
 Conferences The CTK Exchange College math Topic #537 Printer-friendly copy     Email this topic to a friend Reading Topic #537
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?

alexb
Charter Member
1669 posts
Oct-21-05, 06:56 AM (EST)

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), orP(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.shtmlYou 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).