Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 5 - Review - Review Exercises - Page 316: 32f

Answer

The events "Mallory" and "Filters" are not independent because $P(Mallory)\ne P(Mallory~|~Filters)$

Work Step by Step

The sample space: 1009 cases. $So, N(S)=1009$ According to the marginal distribution (see page 235) of the fourth row: $N(Mallory)=186$ Using the Empirical Approach (page 258): $P(Mallory)=\frac{N(Mallory)}{N(S)}=\frac{186}{1009}\approx0.1843$ According to the marginal distribution (see page 235) of the third column: $N(Filters)=120$ According to the cell in the fourth row, third column: $N(Mallory~and~Filters)=40$ $P(Mallory~|~Filters)=\frac{N(Mallory~and~Filters)}{N(Filters)}=\frac{40}{120}=\frac{1}{3}\approx0.3333$ $P(Mallory)\ne P(Mallory~|~Filters)$ The events "Mallory" and "Filters" are not independent (see definition on page 292).
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