Using the axioms of probability, answer whether the following statements are always true or not. If they
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Using the axioms of probability, answer whether the following statements are always true or not. If they are, prove the statement else provide a counterexample. Let A, B, C be subsets of the sample space.
(a) Given A,B are disjoint sets,P(A) +P(B)≤1
(b) Given that B,C are disjoint sets,P(Bc) +P(C)≤1
(c) Given that B,C are disjoint sets,P(B) +P(Bc) +P(C) =P(B∪Bc∪C)
(d) Given that A,B,C are disjoint sets,P(A∪B∪C)> P(A∪B)
(e) P((A∩C)∪(B∩Ac))≤P(A∪B∪C)
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
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