You are at a game show and there are three closed doors. There is a prize hidden behind one of the doors and the game show host knows where it is. You are asked to choose a door. The game show host then opens one of the other two doors showing that it is empty and asks you if you would like to change your selection. Should you stick to your original selection?

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It ought to be reconsidered as the aspect of probabilities have changed.
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Yes stick with my selection.
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There is a 1/3 chance that you'll hit the prize door, and a 2/3 chance that you'll miss the prize. If you do not switch, 1/3 is your probability to get the prize. However, if you missed (and this with the probability of 2/3) then the prize is behind one of the remaining two doors. Furthermore, of these...
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There is a 1/3 chance that you'll hit the prize door, and a 2/3 chance that you'll miss the prize. If you do not switch, 1/3 is your probability to get the prize. However, if you missed (and this with the probability of 2/3) then the prize is behind one of the remaining two doors. Furthermore, of these two, the host will open the empty one, leaving the prize door closed. Therefore, if you miss and then switch, you are certain to get the prize. Summing up, if you do not switch your chance of winning is 1/3 whereas if you do switch your chance of winning is 2/3. read less
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