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Let me try. Say you pick the prize door initially. Obviously, if you switch you will now have a non-prize door. Say you pick one of the two non-prize doors ini
by yellowstuff 10y ago
Let me try. Say you pick the prize door initially. Obviously, if you switch you will now have a non-prize door.
Say you pick one of the two non-prize doors initially. The host now opens the other non-prize door, leaving only the prize door. If you switch you get the prize door.
So switching always changes the prize door to a non-prize door and a non-prize door to the prize door. You start on the prize door 1/3 of the time and a non-prize door 2/3, so you should always switch.
- p1esk 10y agoActually, this makes sense! Thanks.
- deong 10y agoIn teaching a bunch of discrete math classes over the years, I've very rarely found someone for whom the "imagine it's 1000 doors" version helps at all. The only way that gives any insight is if you've already internalized the correct answer. It makes the numbers more extreme; it does nothing to make them make intuitive sense. The version that helped you is the version that helps nearly everyone in my experience.
- diogofranco 10y agoI think the 1000 doors version does help, if you clearly explain the point that "now, if you switch, the only way you lose is if you had guessed the right door out of the 1000!"
- deleted 10y ago[deleted]