Statistics: Informed Decisions Using Data (4th Edition)

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

Chapter 5 - Section 5.4 - Assess Your Understanding - Applying the Concepts - Page 294: 26

Answer

$P(first~is~Yolanda~and~second~is~Lorrie)=\frac{1}{20}=0.05$

Work Step by Step

- First home: The sample space = {Yolanda, Lorrie, Laura, Kim, Anne Marie}. So, $N(S_1)=5$ Now, consider the event "first is Yolanda". $N(first~is~Yolanda)=1$ Using the Classical Method (page 259): $P(first~is~Yolanda)=\frac{N(first~is~Yolanda)}{N(S_1)}=\frac{1}{5}$ - Second home: The sample space = {Lorrie, Laura, Kim, Anne Marie}. So, $N(S_2)=4$ Now, consider the event "second is Lorrie". $N(second~is~Lorrie~|~first~is~Yolanda)=1$ Using the Classical Method (page 259): $P(second~is~Lorrie~|~first~is~Yolanda)=\frac{N(second~is~Lorrie~|~first~is~Yolanda)}{N(S_2)}=\frac{1}{4}$ Now, using the General Multiplication Rule (page 289): $P(first~is~Yolanda~and~second~is~Lorrie)=P(first~is~Yolanda)\times P(second~is~Lorrie~|~first~is~Yolanda)=\frac{1}{5}\times\frac{1}{4}=\frac{1}{20}=0.05$
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