An Introduction to Mathematical Statistics and Its Applications (6th Edition)

Published by Pearson
ISBN 10: 0-13411-421-3
ISBN 13: 978-0-13411-421-7

Chapter 2 Probability - 2.2 Sample Spaces and the Algebra of Sets - Questions - Page 19: 8

Answer

The outcomes in event A are: \[A=\left\{ \begin{align} & SSBBBB,\text{ }SBSBBB,\text{ }SBBSBB,\text{ }SBBBSB,\text{ }BSSBBB, \\ & BSBSBB,BSBBSB,BBSSBB,BBSBSB,BBBSSB \\ \end{align} \right\}\]

Work Step by Step

Event A represents that a batter walks on the sixth pitch. A batter “walks” if the fourth ball is called before the third strike. The umpire can call each pitch either a ball (B) or a strike (S). Hence, the outcomes of event A will contain only 2 strikes (S), and the last pitch is a ball (B). The outcomes of event A are: \[A=\left\{ \begin{align} & SSBBBB,\text{ }SBSBBB,\text{ }SBBSBB,\text{ }SBBBSB,\text{ }BSSBBB, \\ & BSBSBB,BSBBSB,BBSSBB,BBSBSB,BBBSSB \\ \end{align} \right\}\]
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