# Chapter 11 - Counting Methods and Probability Theory - 11.6 Events Involving Not and Or; Odds - Exercise Set 11.6: 85

9:10

#### 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 = $\frac{P(not E)}{P(E)}$ Using the information given to us in the problem, we find the odds against selecting a tragedy or a history. E: {10 history, 10 tragedy} P(E)= $\frac{20}{38}$ = $\frac{10}{19}$ P(not E) = 1 - P(E) = 1 - $\frac{10}{19}$ =$\frac{19 - 10}{19}$ = $\frac{9}{19}$ Odds against E = $\frac{\frac{9}{19}}{\frac{10}{19}}$ = $\frac{9}{10}$

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