# Chapter 11 - Counting Methods and Probability Theory - 11.6 Events Involving Not and Or; Odds - Exercise Set 11.6 - Page 736: 73

25:1

#### 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 black king. E: {2 black kings} P(E) = $\frac{2}{52}$ = $\frac{1}{26}$ P(not E) = 1 - P(E) = 1 - $\frac{1}{26}$ =$\frac{26-1}{26}$ = $\frac{25}{26}$ Odds against E = $\frac{\frac{25}{26}}{\frac{1}{26}}$ = $\frac{25}{1}$

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