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: 25

Answer

$P(I~win)=\frac{1}{324,632}=0.00000308$

Work Step by Step

The sample space: all the combinations of 35 distinct mumbers (from 1 to 35) taken 5 at a time: $N(S)=$ $_{35}C_5=\frac{35!}{5!(30-5)!}=\frac{35!}{5!\times30!}$ But, $35!=35\times34\times33\times32\times31\times(30\times29\times28\times...\times3\times2\times1)=35\times34\times33\times32\times31\times30!$ $_{35}C_5=\frac{35\times34\times33\times32\times31\times30!}{5!\times30!}=\frac{35\times34\times33\times32\times31}{5\times4\times3\times2\times1}=\frac{38955840}{120}=324,632$ With one ticket: $N(I~win)=1$ Using the Classical Method (page 259): $P(I~win)=\frac{N(I~win)}{N(S)}=\frac{1}{324,632}=0.00000308$
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