Monty Hall Problem Analysis

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What is the problem that has dumbfounded people of all shape, size, talent and knowledge? What is the problem that caused scientists to argue ferociously? What is the problem that seems so simple, but can be so hard to understand? What is the problem that can help you understand how probability can deceive you? This problem is called the Monty Hall Problem. Some of you may have heard of this probability problem, based on the game show, “Let’s Make a Deal.” Imagine you are on this game show and Monty Hall, the host, shows you three doors, labelled one, two and three. Behind one of these doors is your dream prize, whether it be money, a brand new car, or a mansion. Behind the other two are “zonks” or goats, in other words, things that you don’t want. You choose a door and let’s say you choose door two. Monty opens number door 1 …show more content…

Let’s say that instead of 3 doors you have 100 and let’s say you pick door number 1. Monty Hall opens all of the doors (which all have goats) except for number 1 and door number 37. Now, do you want to switch? My answer would be YES, because there’s a much, much bigger chance that the car is in door 37, rather than door 1. What can you take away from this problem? How does this show how we think about probability? This experiment demonstrates that probability is really tricky and can easily play games on us. Here is an example: Think about the lottery. Thousands of people invest a few of their dollars each day to buy a lottery ticket. But is it really worth the cost of collectively spending (as a country) $50 billion dollars a year? Many people think that the more lottery tickets you buy, the more likely you are to win the lottery. But, since the tickets are independent of another (they aren’t in any way related to each other) the probability stays the same, similar to a coin toss. The first toss that you do doesn’t affect the second one, and the first lottery ticket that you buy doesn’t affect your second

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