Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 4 - Probability and Counting Rules - 4-3 The Multiplication Rules and Conditional Probability - Extending the Concepts - Page 226: 58



Work Step by Step

For the tortoise to move ahead of the hare, the number on the second die need to be larger than that of the first die. There are three cases (12,13,23). Case 1: $p=\frac{1}{6}\times\frac{2}{6}=\frac{1}{18}$ Case 2: $p=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$ Case 3: $p=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$ The total probability is the sum of all cases which gives $\frac{1}{9}$
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