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: 1


$$S = \{SSS,SSF,SFS,SFF,FSS,FSF, FFS, FFF\}$$ $A = \{SFS, FSS\}$ $B = \{FFF\}$

Work Step by Step

$S$ represents "success" and $F$ represents: "failure". The sample space contains all possibilites of outcome; the first interview can result in $S$ or $F$; the same is true for the second and the third. $$S = \{SSS,SSF,SFS,SFF,FSS,FSF, FFS, FFF\}$$ In the event A, the third interview must be a success; thus, we eliminate: SSF, SFF, FSF, FFF In SSS and FFS, the third interview is not the second success. $A = \{SFS,FSS\}$ In the event B, there is no success; thus, the only outcome possible is FFF $B = \{FFF\}$
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