Elementary Statistics (12th Edition)

Published by Pearson

Chapter 4 - Probability - 4-3 Addition Rule - Basic Skills and Concepts: 32

Answer

$0.3577$

Work Step by Step

We know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$ and by the inclusion-exclusion principle:$P(A \cup B)=P(A)+P(B)-P(A\cap B)$. A:refused B:his/her age is between 18 and 21 or at least 59. By checking the data: $P(A)=\frac{156}{1205}$ $P(B)=\frac{84+251}{1205}$ $P(A\cap B)=\frac{11+49}{1205}$ Therefore the probability of the person responding or his/her age being between 18 and 21: $P(A \cup B)=\frac{156}{1205}+\frac{84+251}{1205}-\frac{11+49}{1205}=\frac{431}{1205}\approx0.3577$

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