Thinking Mathematically (6th Edition)

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 club greater than 4 and less than 10. E: {5,6,7,8,9 of clubs} P(E) = $\frac{5}{52}$ P(not E) = 1 - P(E) = 1 - $\frac{5}{52}$ =$\frac{52-5}{52}$ = $\frac{47}{52}$ Odds against E = $\frac{\frac{47}{52}}{\frac{5}{52}}$ = $\frac{47}{5}$