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<blockquote data-quote="Patryn of Elvenshae" data-source="post: 2334188" data-attributes="member: 23094">Let there exist X doors.&nbsp; One door is the correct choice.The chance of picking the correct door is 1/X.&nbsp; The chance of picking the incorrect door, therefore, is 1-1/X.After you have chosen a door, the set of X doors may be viewed as two subsets: &quot;your door,&quot; and &quot;all other doors.&quot;&nbsp; The chance that subset &quot;your door&quot; is correct is 1/X.&nbsp; The chance that subset &quot;all other doors&quot; is correct is 1-1/X.For any X greater than 2, the chance that subset &quot;all other doors&quot; is correct is greater than the chance that subset &quot;your door&quot; is correct.By way of example, let X = 100.When you randomly choose a door, there is a 1 / 100 chance that you picked correctly (subset &quot;your door&quot;).&nbsp; There is a 99 / 100 chance that you picked incorrectly (i.e., 99% chance subset &quot;all other doors&quot; is correct).When the non-winning doors are removed, you still have the two subsets: &quot;your door&quot; vs. &quot;all other doors.&quot;&nbsp; &quot;All other doors&quot; still has a 99 / 100 chance to be correct.In other words, switching works because you are more likely to be wrong on your first choice than right on your first choice.</blockquote>

[QUOTE="Patryn of Elvenshae, post: 2334188, member: 23094"] Let there exist X doors. One door is the correct choice. The chance of picking the correct door is 1/X. The chance of picking the incorrect door, therefore, is 1-1/X. After you have chosen a door, the set of X doors may be viewed as two subsets: "your door," and "all other doors." The chance that subset "your door" is correct is 1/X. The chance that subset "all other doors" is correct is 1-1/X. For any X greater than 2, the chance that subset "all other doors" is correct is greater than the chance that subset "your door" is correct. By way of example, let X = 100. When you randomly choose a door, there is a 1 / 100 chance that you picked correctly (subset "your door"). There is a 99 / 100 chance that you picked incorrectly (i.e., 99% chance subset "all other doors" is correct). When the non-winning doors are removed, you still have the two subsets: "your door" vs. "all other doors." "All other doors" still has a 99 / 100 chance to be correct. In other words, switching works because you are more likely to be wrong on your first choice than right on your first choice. [/QUOTE]

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