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 that a person who purchased 30 of 5000 raffle tickets will win a trip. P(E) = $\frac{30}{5000}$ = $\frac{3}{500}$ P(not E)= 1- P(E) =1 - $\frac{3}{500}$ =$\frac{500 - 3}{500}$ =$\frac{497}{500}$ Odds against E = $\frac{\frac{497}{500}}{\frac{3}{500}}$ = $\frac{497}{3}$