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Suppose you are doing a multiple choice question with 4 different answers you have no ideas about. You mentally choose one (say A), and as you are about to write that down... you suddenly remember 2 answers that are wrong! And it happens that none of those 2 answers are the one you mentally chose (suppose B and C).

Now, does switching your answer to D increase your chance from 25% to 75%?

SQB
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Saitama
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1 Answers1

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No, because you're not in a situation where you always remember two other wrong answers at the moment you're about to mark your choice.

The analysis in the Monty Hall problem that leads to "it is an advantage to switch" depends on the fundamental assumption that you will be shown a non-prize door that you haven't chosen no matter which choice you made initially.

That does not have much to do with the situation you sketch -- because there's no reason to believe that if you had been about to choose C rather than A, you wouldn't suddenly have had the insight that C is wrong.

hmakholm left over Monica
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  • even it's a different situation, is it possible to prove MATHEMATICALLY our situation gives 50%? – Saitama Dec 06 '13 at 21:48
  • @user42624: Such a proof would need to be based on much more precise assumptions about what can happen in different situations than you have given in your description. "It happens that sucn-and-such" is not a good description of a probabilistic experiment; all possible ways it can play out need to be described such that one can at least imagine carrying it out multiple times. – hmakholm left over Monica Dec 07 '13 at 00:54