Problem: Super Bowl odds. Oddsmakers often list the odds for certain sporting events on the Web. For example, one can find the current odds of winning the next Super Bowl for each NFL team. We found a list of such odds at www.vegas.com/gaming/futures/ superbowl.html. When an oddsmaker says the odds are A to B of winning, he or she means that the probability of winning isB/(A + B). For example, when we checked the Web site listed above, the odds that the Indianapolis Colts would win Super Bowl XLIV were 13 to 2. This corresponds to a probability of winning of 2/(13 + 2) =2/15. On the Web, find the current odds, according to an oddsmaker, of winning the Super Bowl for each NFL team.
Required:
1. Convert these odds to probabilities. Do these probabilities satisfy Rules 1 and 2 given in this chapter? If they don't, can you think of a reason why?