Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 7 - Section 7.3 - Probability and Probability Models - Exercises - Page 486: 104

Answer

$P(A\cup B\cup C\cup D)=P(A)+P(B)+P(C)+P(D)-3P(A\cap B\cap C \cap D)$

Work Step by Step

The intersection between the four events is such that: $P(A\cap B\cap C \cap D)=P(A\cap B)=P(A\cap C)=P(A\cap D)=P(B\cap C)=P(B\cap D)=P(C\cap D)=P(A\cap B\cap C)=P(A\cap B\cap D)=P(A\cap C\cap D)=P(B\cap C\cap D)$ So, when we add $P(A)+P(B)+P(C)+P(D)$ we add the intersection $P(A\cap B\cap C \cap D)$ four times. So, it needs to be removed three times.
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