So there's three doors, A, B and C, and behind one of them is a hot girl (or hot guy (your choice)) who will love you forever if you pick the right door
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If the voice is telling the truth, its always better to switch doors. Think of it like this: there are a million doors, and you pick number one. The voice says the person is not behind the doors numbered three through one million. Isn't it a good idea to switch to door number two at this point?
Re: Switch Doorszirilan717May 3 2005, 02:49:14 UTC
That is an excellent analogy, with 3 doors it makes it more difficult to see how the probability would change to 2/3, not 1/2 like Erik thought it would. With a million the probability would change to PICK THE OTHER DOOR!!
so for your initial selection there's a 33% chance you're right.
if you assume the voice wouldn't eliminate the real one, then after they eliminate door C, there are two possibilities: you were right or you were wrong.
there's still a 33% chance you were right, but if you were wrong then the voice would have had to eliminate the only other wrong door, meaning the third door has to be the right one, meaning that if you were wrong initially you'd have to be right when you switched. so for the 2/3 likelihood that you were wrong the first time, there's a 100% chance if you switch you'll be right.
that makes the overall odds if you switch 2/3, as opposed to the 1/3 for your initial choice. get it?
but once C has been eliminated, i dont see why the final probablities are diffrent between A and B... like your intial probability is 1/3 for A, but when C is outlawed, then A and B become equal, no matter what you chose before. sorta like no matter how many times you flip a coin, the chance on the next flip is still 50 50..
Re: Switch Doorszirilan717May 5 2005, 01:43:11 UTC
It is slightly different Jessy, because you have to realize that the choice was made BEFORE the door was open. When you choose door B, the probability is 1/3. This means the probability of he/her being behind doors A or C is 2/3. When Door C is eliminated, it makes it so the probabiltiy is still the same, 1/3 behind B, and 2/3 behind A or C (now A). Your analogy, although often used for statistics, isn't sequitor for this question. If door C was eliminated, and then the girl was placed randomly behind door A or B, THEN the probability would be 1/2 for each door, and it wouldn't matter. However, since the girl stays put where she is at the beginning of the problem, it is 1/3 for B, 2/3 for A.
Re: Switch DoorssammyduboffMay 4 2005, 19:24:39 UTC
yeah-- sorry dan-- i know it's your question, but we did this problem in class. clayton has the right odds and eliane's analogy is good. unless you are making a 'funny' answer, like you should open both doors.
~Eliane
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if you assume the voice wouldn't eliminate the real one, then after they eliminate door C, there are two possibilities: you were right or you were wrong.
there's still a 33% chance you were right, but if you were wrong then the voice would have had to eliminate the only other wrong door, meaning the third door has to be the right one, meaning that if you were wrong initially you'd have to be right when you switched. so for the 2/3 likelihood that you were wrong the first time, there's a 100% chance if you switch you'll be right.
that makes the overall odds if you switch 2/3, as opposed to the 1/3 for your initial choice. get it?
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