CASE STUDY Shortly after the New England Patriots won Super Bowl XLIX, websites were already posting the probabilities of winning Super Bowl 50 for the various NFL teams. These probabilities were updated regularly. Table 18.1 lists the probabilities posted on one website on September 21, 2015. These are perhaps best interpreted as personal probabilities. They are likely to change as the 2015 season progresses because the players on teams will change due to trades and injuries.

Because these are personal probabilities, are there any restrictions on the choices for the probabilities? In this chapter, we will answer this question. We will learn that probabilities must obey certain rules in order to make sense. By the end of this chapter, you will be able to assess whether the probabilities in Table 18.1 make sense.