Hey guys, I need some help on this problem please

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Verify the following extension of the addition rule by a) an appropriate Venn diagram and b) by a formal argument using the axioms of probability and the propositions in the chapter.

$\displaystyle P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C) - P(B \cap C) + P(A \cap B \cap C)$

I don't understand the last part which says: $\displaystyle + P(A \cap B \cap C)$ because they are now adding some of the same elements twice. But the question does say VERIFY and not prove...

2. $\displaystyle A \cap B \cap C$ is the intersection between the three sets A, B and C

The following Venn diagram may be of help:

3. Originally Posted by colby2152
$\displaystyle A \cap B \cap C$ is the intersection between the three sets A, B and C

The following Venn diagram may be of help:
Ah i get it now! After we removed the intersections of A and B, A and C, etc, then we have removed an essential part of the circles, namely where they all intersect, and we have to add that part again.

Thanks Colby!