Betting odds are usually stated against the event happening (against winning).
The odds against event W are the ratio

In horse racing, the betting odds are based on the probability that the horse does not win.
(a) Show that if we are given the odds against an event W as a:b, the probability of not W is P(Wc) = a/a + b. Hint: Solve the equation

for P(Wc).
(b) In a recent Kentucky Derby, the betting odds for the favorite horse, Point Given, were 9 to 5. Use these odds to compute the probability that Point Given would lose the race. What is the probability that Point Given would win the race?
(c) In the same race, the betting odds for the horse Monarchos were 6 to 1. Use these odds to estimate the probability that Monarchos would lose the race. What is the probability that Monarchos would win the race?
(d) Invisible Ink was a long shot, with betting odds of 30 to 1. Use these odds to estimate the probability that Invisible Ink would lose the race. What is the probability the horse would win the race? For further information on the Kentucky Derby, visit the Brase/Brase statistics site at www.cengagebrain .com and find the link to the Kentucky Derby.

Transcribed Image Text:

P(not W) P(W) P(W) P(W) a P(W)