‘Odds’ in horserace betting are defined as follows: 3/1 (three-to-one against) means a horse is expected to win once for every three times it loses; 3/2 means two wins out of five races; 4/5 (five to four on) means five wins for every four defeats, etc.

(a) Translate the above odds into ‘probabilities’ of victory.

(b) In a three-horse race, the odds quoted are 2/1, 6/4, and 1/1. What makes the odds different from probabilities? Why are they different?

(c) Discuss how much the bookmaker would expect to win in the long run at such odds, assuming each horse is backed equally.