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: 59

Answer

61:10; 10:61

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 = $\frac{P(E)}{P(not E)}$ Find the odds in favor and the odds against a person in the military population being a man. P(E)= $\frac{1220000}{1420000}$ = $\frac{122}{142}$ = $\frac{61}{71}$ P(not E) = 1 - P(E) = 1 - $\frac{61}{71}$ =$\frac{71 - 61}{71}$ = $\frac{10}{71}$ Odds in Favor = $\frac{\frac{61}{71}}{\frac{10}{71}}$ = $\frac{61}{10}$ 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 = $\frac{P(not E)}{P(E)}$ Odds against E = $\frac{\frac{10}{71}}{\frac{61}{71}}$ = $\frac{10}{61}$ The odds against E can also be found by reversing the ratio representing the odds in favor of E.
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