Author: Omid David
Date: 02:53:07 09/28/02
We have to understand what the "switch" operation does here: If our first choice was correct, it will turn it into false; and if our first choice was false, it will turn into correct. So in order to eventually succeed, we have to initially choose the correct door in "stay" method, and the *wrong* door in "switch" method. Thus, the operation "switch" merely "negates" the probability, i.e. if the initial probability was x%, it will now become (100-x)%. For n doors, the success probability of "stay" will be (100/n)%, and the success probability of "switch" will be (100 - 100/n)%. Examples: In the case of 3 doors, the initial probability was 33% (x=33), so after the "switch" operation, it will become 67% (100-33=67). For 10,000 doors, the success probability of "switch" will be 99.99%, while "stay" will only have a 0.01% probability of success. In Marilyn vos Savant's example with 777,777 doors, the probability of success with "switch" will be 99.99987%. Omid.
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