Applied Statistics and Probability for Engineers, 6th Edition

Published by Wiley
ISBN 10: 1118539710
ISBN 13: 978-1-11853-971-2

Chapter 2 - Section 2-3 - Addition Rules - Exercises: 2-83

Answer

(a) 0.9 (b) 0 (c) 0 (d) 0 (e) 0.1

Work Step by Step

Since they are mutually exclusive events: A ∩ B = A ∩ C = B ∩ C = Ø and P(A ∩ B) = P(A ∩ C) = P(B ∩ C) = 0 (a) P(A U B U C) = P(A) + P(B) + P(C) = 0.2 + 0.3 + 0.4 = 0.9 (b) P(A ∩ B ∩ C) = P[(A ∩ B) ∩ C] = P(Ø ∩ C) = 0 (c) P(A ∩ B) = 0 (d) P[(A U B) ∩ C] = P[(A ∩ C) U (B ∩ C)] = 0 (e) P(A' ∩ B' ∩ C') = 1 - P(A) - P(B) - P(C) = 1 - 0.2 - 0.3 - 0.4 = 0.1
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