Probability of the union of $3$ events? I need some clarification for why the probability of the union of three events is equal to the right side in the following:
$$P(E\cup F\cup G)=P(E)+P(F)+P(G)-P(E\cap F)-P(E\cap G)-P(F\cap G)+P(E\cap F\cap G)$$
What I don't understand is, why is the last term(intersection of all) added back just once, when it was subtracted three times as it appears from a Venn Diagram?
Here on page 3, this is explained but not in enough details that I can understand it:
http://www.math.dartmouth.edu/archive/m19w03/public_html/Section6-2.pdf


Since in this formula you add this part 3 times(in the first 3 terms) and subtract it also 3 times(in the next 3 terms), you have to add it again.
