1. The problem statement, all variables and given/known data Prove the general inclusion-exclusion formula. 2. Relevant equations Inclusion-exclusion Formula: P(C1 U C2 U...U Ck) = p1 - p2 + p3 - ... + (-1)(k+1)pk where pi equals the sum of the probabilities of all possible intersections involving i sets. 3. The attempt at a solution Assume that the formula holds for n sets. Then for n+1 sets... P(union k=1 to n+1 of Ck) = P((union k=1 to n of Ck) union Cn+1) = P(union k=1 to n of Ck) + P(Cn+1) - P((union k=1 to n of Ck) intersect Cn+1) = P(union k=1 to n of Ck) + P(Cn+1) - P(union k=1 to n of (Ck intersect Cn+1)) = sum k=1 to n of P(Ck) + P(Cn+1).... From there I don't know how to show the alternating pattern.