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: 72

Answer

12:1

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 5. E: {4 cards that are 5's} P(E) = $\frac{4}{52}$ = $\frac{1}{13}$ P(not E) = 1 - P(E) = 1 - $\frac{1}{13}$ =$\frac{13-1}{13}$ = $\frac{12}{13}$ Odds against E = $\frac{\frac{12}{13}}{\frac{1}{13}}$ = $\frac{12}{1}$
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