Monty Hall Problem Simulation
Since a lot of university mathematicians, engineers, and physicists famously got the answer wrong, I&#x27;ve classified The Monty Hall Problem as more of an &quot;English parsing&quot; problem instead of a math problem.  From wikipedia[1], the problem as stated:<p><i>&gt;&quot;Suppose you&#x27;re on a game show, and you&#x27;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&#x27;s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, &quot;Do you want to pick door No. 2?&quot; Is it to your advantage to switch your choice?&quot;</i><p>The key phrase that everyone glosses over is: <i>&quot;, and the host, who knows what&#x27;s behind the doors, opens another door, say No. 3, which has a goat.&quot;</i><p>If it was reworded as <i>&quot;the host who knows what&#x27;s behind the doors and _always_ opens the door with a goat and _never_ opens the door with the car&quot;</i>, the mathematicians would have seen the 2&#x2F;3rds probability.  The original wording with the nonchalant <i>&quot;say&quot;</i> in the middle of <i>&quot;, opens another door, _say_ No. 3, which has a goat&quot;</i> makes it seems like there was no link between the host&#x27;s knowledge of what&#x27;s behind the door and the opening of door #3 and therefore <i>random</i>.  Therefore, the 50&#x2F;50 probability seemed to be the correct answer.<p>[1] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Monty_Hall_problem" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Monty_Hall_problem</a>