## Thinking Mathematically (6th Edition)

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 woman. P(E)= $\frac{200000}{1420000}$ = $\frac{20}{142}$ = $\frac{10}{71}$ P(not E) = 1 - P(E) = 1 - $\frac{10}{71}$ =$\frac{71 - 10}{71}$ = $\frac{61}{71}$ Odds in Favor = $\frac{\frac{10}{71}}{\frac{61}{71}}$ = $\frac{10}{61}$ 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 = $\frac{\frac{61}{71}}{\frac{10}{71}}$ = $\frac{61}{10}$ The odds against E can also be found by reversing the ratio representing the odds in favor of E.