Odds of winning a horse race. Handicappers for horse races express their beliefs about the...

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 – P(E). 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  to , or 1 to 3. It follows that the odds against E are 1 – P(E) 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 P(E) = a/(a + b).

a. A second handicapper assesses the probability of a win by Smarty Jones to be 1/3. According to the second handicapper, what are the odds in favor of a Smarty Jones win?

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b. A third handicapper assesses the odds in favor of Smarty Jones to be 1 to 1. According to the third handicapper, what is the probability of a Smarty Jones win?

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c. A fourth handicapper assesses the odds against Smarty Jones winning to be 3 to 2. Find this handicapper’s assessment of the probability that Smarty Jones will win.