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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: The Darn Old Cocked Hat - the sequel 1
From: Luc Van den Borre
Date: 2013 Mar 17, 21:12 +0100
From: Luc Van den Borre
Date: 2013 Mar 17, 21:12 +0100
On 17/03/2013 20:17, Tom Sult wrote: > ------------------------------------------------------------------------ > This explanation is a commonly held view but I think it is in error. > These are really two independent events. The first was a choice of > three. The second was a nonrandom elimination of one of the choices. > This makes the second event an independent choice of one out of two. > Therefore keeping your current curtain or changing to the other curtain > results in the same 50-50 probability. I still remember the shame of getting this wrong in front of a hundred people at university, so I'll take a stab at explaining it. Imagine you do this experiment many times. You always choose door A as your initial choice. How often will you be correct if you stick with it? Obviously, since the prize is placed randomly, over many iterations door A will be the correct 1/3 of the time. So not switching doors has a 1/3 chance of winning the prize. Monty doesn't move the prize around! Now, imagine you choose door A at first, but switch to the remaining door after Monty opens B or C. - One third of the time, the prize is behind A, Monty opens an empty door and you switch to the other empty door. Bad luck. - One third of the time, the prize is behind B, Monty opens C, and you switch to B to win the prize. - One third of the time, the prize is behind C, Monty opens B, and you switch to C to win the prize. So in conclusion, by switching you win 2/3 of the time, whereas by sticking with your initial choice you win 1/3 of the time. By the way, hello everyone! I recently got interested in celestial navigation on land. Most of the discussion so far is slightly over my head (badoom tish!). Luc Van den Borre