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: 75



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 find the odds against drawing a spade greater than 3 and less than 9. E: {4,5,6,7,8 of spades} P(E) = $\frac{5}{52}$ P(not E) = 1 - P(E) = 1 - $\frac{5}{52}$ =$\frac{52-5}{52}$ = $\frac{47}{52}$ Odds against E = $\frac{\frac{47}{52}}{\frac{5}{52}}$ = $\frac{47}{5}$
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