I'm confused :/
P(X,Y,Z) = P(X,(Y,Z)) = P(X) + P(Y,Z) - P(X;(Y,Z)) = P(X) + (P(Y) + P(Z) - P(Y;Z)) - P(X;(Y,Z)) = P(X) + (P(Y) + P(Z) - P(Y;Z)) - P((X;Y),(X;Z)) = P(X) + (P(Y) + P(Z) - P(Y;Z)) - (P(X;Y) + P(X;Z) - P(X;Y;Z)) = P(X) + P(Y) + P(Z) - P(X;Y) - P(Y;Z) - P(X;Z) + P(X;Y;Z)
By the inclusion-exclusion principle, no?
http://www.wired.com/science/discoveries/news/2008/02/boarding