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

1 Answer
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!