 Let us look now at the strategy accounting for all possibilities. This technique in general is extremely impractical, like if you needed to list all the possible license plates in North Carolina to solve a particular problem. However it is very practical when the possibilities are few and in fact sometimes it is THE best strategy. Consider the following problem, also known as the Monty Hall problem. At a game show you are given the choice of three doors. Behind one door is a car and behind the other door is goats. After you pick a door, the host who knows what is behind the doors opens another door and reveals a goat. He then asks you whether you wish to switch your choice. Is it to your advantage to do that? Many mathematicians, including some of the greatest mathematicians of the 20th century like Paul Erdisch, were baffled by this problem at first. We can look at it this way. We have three doors, let us call them A, B and C. You choose one door, say A. And now the host opens a door and shows you a goat, maybe shows B and here is a goat. And now the problem is, should you switch doors? Should you choose now C or should you stick with A? Let us use the technique of accounting for all possibilities. There are three possible outcomes. You choose the correct door, although you are not aware of it, and you switch, in which case you lose. But you may choose one wrong door and switch, in which case you win. Or you may choose the other wrong door and switch, in which case you also win. So in two out of these three possibilities, you win. So the probability of winning is two-thirds. So it is to your advantage to switch. Thank you.