Let A1, A2, and A3 be three events in a sample space , which are not necessarily
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Let A1, A2, and A3 be three events in a sample space Ω, which are not necessarily pairwise disjoint.
(i) Prove that P(A1 ∪ A2 ∪ A3) ≤ P(A1) + P(A2) + P(A3).
(ii) Show that the equality P(A1 ∪ A2 ∪ A3) = P(A1) + P(A2) + P(A3)
holds if and only if P(A1A2) + P(A1A3) + P(A2A3) = P(A1A2A3).
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Related Book For 
Introduction To Probability Volume 2
ISBN: 9781118123331
1st Edition
Authors: Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis
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