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Puzzle 2.5 illustrates the Monty Hall problem; it is based on the American game show Let’s Make a Deal and the name of the problem comes from the show’s host, Monty Hall.
Suppose that you are on a game show, and you’re given the choice of three boxes. One of them contains an expensive prize (the latest Ferrari), whereas the other two boxes are empty. Of course, you do not know which box contains the car. You are asked to select one of the boxes, which you do. The game show host, who knows which box contains the car, opens one of the other empty boxes (note that there is at least one empty box among the two remaining boxes). Now you are told to make your final selection: you can stay with your original choice or switch to the other unopened box. Whatever you do, this is your final selection and you get what is in that box. What should you do? Should you stay with your original guess or switch to the other box?
Make a few experiments where you stay with the original choice followed by another set of experiments where you always switch. You should see a significant difference in your success rate (i.e., of picking Ferrari) in one of these strategies …