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: 83

Answer

14:5

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 = $\frac{P(E)}{P(not E)}$ Using the information given to us in the problem, we find the odds in favor of selecting a comedy or a tragedy. E: {18 comedies, 10 tragedies} P(E)= $\frac{28}{38}$ = $\frac{14}{19}$ P(not E) = 1 - P(E) = 1 - $\frac{14}{19}$ =$\frac{19 - 14}{19}$ = $\frac{5}{19}$ Odds in Favor = $\frac{\frac{14}{19}}{\frac{5}{19}}$ = $\frac{14}{5}$
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