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##### Monty Hall Problem with Maple 17

**Description**

solution

**Question**

Let's say you wanted to solve once and for all the Monty Hall Problem;Suppose you're on a game show, and you're given the choice of three doors;Behind one door is a car, behind the others, goats. You pick a door, say No. 1;and the host, who knows what's behind the doors, opens another door, say No.;3, which has a goat. He then says to you, \Do you want to pick door No. 2?" Is;it to your advantage to switch your choice?;This problem has been debated for years. If you look it up on the web, you can find various;explanations of why it is better to switch your choice. The proof by using probability is not;obvious, so we will use our method of random number simulations to explore the following;questions;The first part of your final project is to provide evidence of why you should switch;your choice in the three door game by using random number simulations.;The second part of project is to perform a similar experiment using a total of four;doors. (Only one has a car. The rest have goats.) In this case, there are two rounds;of opening a door (showing a goat) and each time you have the opportunity to switch;your choice. By simulation, can you determine the "\most winning" strategy? It can;be a combination of switching or not switching in those two steps.;Can you extend your result to games with more doors? Do you think there is a pattern;as you add more doors?;A complete report would have the following outline;Three Door Problem;{ Describe the problem. Look up an explanation of the (theoretical) probability of;winning for each choice and describe the reasoning in your own words.;{ Set up an experiment (simulation) for this game. Provide a copy of the code in;the Appendix.;{ Approximate the number of wins per total games for the switching strategy. Make;sure to report the number of simulations you used and repeat the experiment to;verify the results. Does this match the probability you predicted above?;{ Approximate the number of wins per total games for the NOT switching strategy.;Does this match the probability you predicted above?;{ Summarize your results and how they support your winning strategy.;Four Door Problem;{ Describe the problem and the possible switching strategies in your own words.;{ Set up an experiment (simulation) for this game. Provide a copy of the code in;the Appendix.;{ Approximate the number of wins per total games for each switching strategy.;Make sure to report the number of simulations you used and repeat the experiment;to verify the results.;{ From your data, conclude which is the best strategy. Can you explain why this;is true?;{ Can you extend your winning strategy to more doors? Why does it make sense?

Paper#71052 | Written in 18-Jul-2015

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