 The above result may seem remarkable; in particular, the fact that a person’s preferences can determine a unique probability function that represents her beliefs. On a closer look, however, it is evident that some of our beliefs can be determined by examining our preferences. Suppose you are offered a choice between two lotteries, one that results in you winning a nice prize if a coin comes up heads but getting nothing if the coin comes up tails, another that results in you winning the same prize if the coin comes up tails but getting nothing if the coin comes up heads. Then assuming that the desirability of the prize (and similarly the desirability of no prize) is independent of how the coin lands, your preference between the two lotteries should be entirely determined by your comparative beliefs for the two ways in which the coin can land. For instance, if you strictly prefer the first lottery to the second, then that suggests you consider heads more likely than tails.