He will seek a rule which is a reasonable diagnostic for the problem, but which is unlikely to be guessed in advance by his students. He certainly makes mistakes, but he guesses correctly most of the time. Toss a coin n times, and call the length of the longest run of heads L n . You might also like to look at the coin-flipping puzzle for an explanation of this relationship. An unusually long run of heads is an example of a 'rare event'.
Rare events can be important for ordinary people.
For example, a very high tide is a rare event, but it can cause enormous flood damage in countries such as Holland. Inhabitants of low countries invest a lot of money in protection against such events, by building dams for flood protection, even though the chance of such an event is small. Insurance companies need to assess the chances and costs of major catastrophes, even though such events are rare. These companies employ actuaries to do this work, and these people use statistics and probability in their day to day work. Major falls in the Stock Exchange are rare, and can be associated with gigantic effects on the worldwide market.