Probability, rarity, interest, and surprise.

THE unusual is often interesting. Moreover, the frequency definition of probability, which is the one consciously or tacitly used in all applications to experience, makes it clear that an improbable event means precisely a rare event. Hence, an improbable event is often interesting. But is an improbable event always interesting? We shall see that is is not. If an event actually occurs, and if its probability, as reckoned before its occurrence, is very small, is the fact of its occurrence surprising? The answer is that it may be, or it may not be. Suppose one shuffles a pack of cards and deals off a single bridge hand of thirteen cards. The probability, as reckoned before the event, that this hand contain any thirteen specified cards is 1 divided by 635,013,559,600. Thus the probability of any one specified set of thirteen cards is, anyone would agree, very small. When one hand of thirteen cards is dealt in this way there are, of course, precisely 635,013,559,600 different hands that can appear. All these billions of hands are, furthermore, equally likely to occur; and one of them is absolutely certain to occur every time a hand is so dealt. Thus, although any one particular hand is an improbable event, and so a rare event, no one particular hand has any right to be called a surprising event. Any hand that occurs is simply one out of a number of exactly equally likely events, some one of which was bound to happen. There is no basis for being surprised at the one that did happen, for it was precisely as likely (or as unlikely, if you will) to have happened as any other particular one.