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When you select the door, you partition the set of doors into two subsets, the door you chose and the doors that you did not choose. At this stage the probabilities of the prize being in the partitions is fixed - 1/3 for the door you chose, 2/3 for those that you did not. The new information introduced with the revealing of the goat behind one of the doors in set 2, only pertains to that second set, the information you have on the first set remains fixed. On the other hand, you now have a 2/3 probability on the second set with only one door remaining (in that set).


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