Odds

Let the probability of the occurrence of an event be denoted by p, thereby implying that 1 - p represents the probability of the nonoccurrence of the event. Succinctly, the odds of the occurrence of the event are defined as the ratio of the probability of the occurrence to the probability of the nonoccurrence, or .

Odds are often encountered in gambling situations. A pertinent example can be extracted from a football game. For instance, if a Vegas odds maker assigns an 80% probability of a football team from western New York winning a match against another team from eastern Massachusetts, the suggested odds of the football team from western New York winning are .

If the odds can be represented in terms of a fraction , ...