Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 11 - Counting Methods and Probability Theory - 11.6 Events Involving Not and Or; Odds - Exercise Set 11.6 - Page 736: 63



Work Step by Step

The odds against E are found by taking the probability that E will not occur and dividing by the probability that E will occur. Odds against E = $\frac{P(not E)}{P(E)}$ We are asked to find the odds against rolling a number greater than 2. S: {1,2,3,4,5,6} E: {3,4,5,6} P(E)= $\frac{4}{6}$ = $\frac{2}{3}$ P(not E) = 1 - P(E) = 1 - $\frac{2}{3}$ =$\frac{3-2}{3}$ = $\frac{1}{3}$ Odds against E = $\frac{\frac{1}{3}}{\frac{2}{3}}$ = $\frac{1}{2}$
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