This is a very famous problem which has led to many arguments over the years. There is a very important lesson about statistics in this one. You are a Game Show contestant. You are shown three doors. |
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It can be yours - all you have to do is choose the right door! Behind the other two are a toy bear. Cute he might be, but he isn't quite what you want given there is a car behind one of the doors. |
Your compere is Monty Hall. He asks you to choose a door. You do so. He then opens one of the other doors to reveal a toy bear. This is what he does every time someone plays the game. He then asks you if you want to change your mind.
Have you a higher probability of winning if you stick with your original choice? Or if you change to the other closed door? Or doesn't it make any difference? What is your reasoning? |
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The problem has been presented in a number of formats over the years. Martin Gardner, in his great Scientific American column, presented it decades ago. The best known was presented in 1990 by the person reputed to have the highest IQ ever measured, Marilyn vos Savant, who wrote about it in American Parade Magazine. There she referred to the real American game show, Let's Make A Deal hosted by Monty Hall. Monty Hall really did have a car and, instead of toy bears, he had live goats! A huge debate followed with many mathematicians disputing her solution.
This is a much discussed problem. So what do you think?
Should you change your choice?