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: 62

Answer

2:1

Work Step by Step

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