Often, probabilities are expresscd in terms of odds. especially in gambling settings. For example, handicappers for greyhound races express their belief about the probabilities that each greyhound will win a race in terms of odds. If the probability of evcnt 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 Oxford Shoes will win its next race, the odds in favor of Oxford Shoes are '5/1nn to 7-5/100, 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 Oxford Shoes. In general, if the odds in favor of event EJ are n to

b, thcn P(E) =

a/(u + 0).

a. A second handicapper assesses the probability of a win by Oxford Shoes to be y3. According to the second handicapper, what are the odds in favor of Oxford Shoes winning?

b. A third handicapper assesses the odds in favor of Oxford Shoes to be 1 to 1. According to the third handicapper, what is the probability of OxCord Shoes winning?

c. A fourth handicapper assesses the odds against Oxford Shoes winning to be 3 to 2. Find this handicapper's assessment of the probability that Oxford Shoes will win.