Odds of winning a horse race. Handicappers for horse races express their beliefs about the probability of each horse winning a race in terms of odds. If the probability of event E is P(E ), then the odds in favor of E are P(E )

to 1 - P1E2. Thus, if a handicapper assesses a probability of .25 that Smarty Jones will win the Belmont Stakes, the odds in favor of Smarty Jones are 25100 to 75100, or 1 to 3.

It follows that the odds against E are 1 - P1E2 to P(E ), or 3 to 1 against a win by Smarty Jones. In general, if the odds in favor of event E are a to

b, then P1E2 = a> 1a + b2.

a. A second handicapper assesses the probability of a win by Smarty Jones to be 15. According to the second handicapper, what are the odds in favor of a Smarty Jones win?

b. A third handicapper assesses the odds in favor of Smarty Jones to be 2 to 3. According to the third handicapper, what is the probability of a Smarty Jones win?

c. A fourth handicapper assesses the odds against Smarty Jones winning to be 5 to 3. Find this handicapper’s assessment of the probability that Smarty Jones will win.