Sample Space, Events and Probability
(v) For any events E and F, P(E [F) = P(E)+P(F) P(E \F). (vi) For any n 2 and any events E 1;:::;E n, P([n i=1E i) = Xn i=1 P(E i) X i 1<i 2 P(E i 1 \E i 2)+ +( 1) k+1 X i 1< <i k P(\k j=1E i j)+ +( 1) n+1P(\n i=1E i): The last formula is called the inclusion-exclusion formula. Proof. We are only going to prove (i), (ii), (v). (vi) follows from ...
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