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The Monty Hall problem explained

The Monty Hall problem is a classic probability puzzle that has puzzled mathematicians and game show contestants for decades. The problem is based on a game show called Let's Make a Deal, hosted by Monty Hall, which was popular in the 1960s and 1970s. The problem has become famous because it is counterintuitive and seemingly goes against our common sense understanding of probability. The problem is presented as follows: You are a contestant on a game show, and there are three doors in front of you. Behind one of the doors is a valuable prize, such as a car, and behind the other two doors are goats. You are asked to choose one of the three doors, and after you have made your choice, Monty Hall, the host, opens one of the other two doors to reveal a goat. He then asks you if you want to switch your choice to the remaining door or stick with your original choice. What should you do? At first glance, it may seem that the probability of winning the prize is 1 in 3, and there
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