Reference no: EM132381318

Let A,B, and C be three events. Let AB denote the intersection of A and B, so AB = A ∩ B, and let ABC denote the intersection A, B, and C, so ABC = A ∩ B ∩ C. Use the additivity axiom and appropriate partitioning of the event A ∪ B ∪ C to derive the following inclusion-exclusion formula for the probability of a union of three events:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(AB) - P(AC) - P(BC) + P(ABC).