Prove that? : #P(AuuBuuC)=P(A)+P(B)+P(C)-P(AnnB)-P(BnnC)-P(AnnC)+P(AnnBnnC)#

#P(AuuBuuC)=P(A)+P(B)+P(C)-P(AnnB)-P(BnnC)-P(AnnC)+P(AnnBnnC)#

I can show that with diagram, but how to prove it with formulas?

https://www.quora.com/What-is-n-AUBUC-equal-to

1 Answer
Ratnaker Mehta
Aug 7, 2018

Please refer to The Explanation.

Explanation:

#"Prerequisite : "P(AuuB)=P(A)+P(B)-P(AnnB)....(star)#.

#P(AuuBuuC)=P(AuuD)," where, "D=BuuC#,

#=P(A)+P(D)-P(AnnD)..........[because, (star)]#,

#=P(A)+color(red)(P(BuuC))-color(blue)(P[Ann(BuuC)])#,

#=P(A)+color(red)(P(B)+P(C)-P(BnnC))-color(blue)(P(AnnB)uu(AnnC)),#

#=P(A)+P(B)+P(C)-P(BnnC)-color(blue){[P(AnnB)+P(AnnC)-P((AnnB)nn(AnnC)]#,

#=P(A)+P(B)+P(C)-P(AnnB)-P(BnnC)-P(AnnC)+P(AnnBnnC),#

as desired!

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