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<blockquote data-quote="imhotep" data-source="post: 30654077" data-attributes="member: 562115"><p>The origin of this problem dates back to 1889. It's a variation of <strong>Bertrand's Boxes problem</strong>. Bertrand offered the solution, arrived at the correct answer but his thinking was flawed.</p><p>Also Martin Gardner's <strong>Three Prisoners Problem </strong>is another mathematically equivalent problem.</p><p></p><p>There are many ways to solve the Monty Hall problem and possibly the simplest is to use Bayes' Theorem. </p><p></p><p>The flaw in thinking stems from the fact that most are <strong>not taking Monty's filtering into account, thinking the chances are the same before and after</strong>. So it becomes a Statistical illusion.</p><p></p><p>There are many simulations, two are listed below.</p><p></p><p><a href="https://www.mathwarehouse.com/monty-hall-simulation-online/" target="_blank">https://www.mathwarehouse.com/monty-hall-simulation-online/</a></p><p><a href="https://montyhall.io/" target="_blank">https://montyhall.io/</a></p></blockquote><p></p>
[QUOTE="imhotep, post: 30654077, member: 562115"] The origin of this problem dates back to 1889. It's a variation of [B]Bertrand's Boxes problem[/B]. Bertrand offered the solution, arrived at the correct answer but his thinking was flawed. Also Martin Gardner's [B]Three Prisoners Problem [/B]is another mathematically equivalent problem. There are many ways to solve the Monty Hall problem and possibly the simplest is to use Bayes' Theorem. The flaw in thinking stems from the fact that most are [B]not taking Monty's filtering into account, thinking the chances are the same before and after[/B]. So it becomes a Statistical illusion. There are many simulations, two are listed below. [URL]https://www.mathwarehouse.com/monty-hall-simulation-online/[/URL] [URL]https://montyhall.io/[/URL] [/QUOTE]
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