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Kyrall
A Few Killers
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Posted - 2008.09.09 15:14:00 -
[1]
You are a contestant in a game show. There are 3 doors: 2 hide goats, one hides a car. If you choose the door hiding the car, you keep the car. If you choose a goat-door, you don't keep it, you just lose. The goats are only for effect. In fact, forget the goats. Those doors are now empty.
When you make your choice, I reveal a goat (at least one of the other doors must obviously hide a goat) and you now have a second chance to pick a door. The question is this:
Do you swap to the remaining door or keep your first choice? Does it even matter?
If you already know of the problem, please refrain from posting the answer too soon, it would spoil the fun. I want to see more heated arguments! 
_____ Originally by: Pwett
You sir, underestimate the things I have and will pee on.
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pwnedgato
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Posted - 2008.09.09 15:17:00 -
[2]
Reserved
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Shadowsword
COLSUP
Tau Ceti Federation
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Posted - 2008.09.09 15:18:00 -
[3]
I wouldn't swap, statistically it wouldn't improve your chances.
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Kyrall
A Few Killers
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Posted - 2008.09.09 15:35:00 -
[4]
Originally by: Shadowsword
I wouldn't swap, statistically it wouldn't improve your chances.
Care to elaborate? Please work through your logic for people to follow and agree/disagree/improve upon.
_____ Originally by: Pwett
You sir, underestimate the things I have and will pee on.
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Xtreem
Gallente
Interstellar Brotherhood of Gravediggers
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Posted - 2008.09.09 15:41:00 -
[5]
i done this for college, mathmatics The Monty Hall Paradox
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ReaperOfSly
Gallente
Lyrus Associates
The Star Fraction
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Posted - 2008.09.09 15:44:00 -
[6]
Edited by: ReaperOfSly on 09/09/2008 15:46:48
Originally by: Shadowsword
I wouldn't swap, statistically it wouldn't improve your chances.
WRONG!!! 
Edit: always swap. If you swap, you have a 66% chance of getting the car, if you don't, you have 33% chance of getting the car. Remember, when you first choose, you have a 33% chance of getting it right. The presenter ALWAYS knows what's behind the doors and will open any door which has a goat behind it. The chance that the door you picked originally is correct is STILL only 33%, so swapping your choice to the other door doubles your chances.
QED. 
__________________________
Quote:
...bored, skint, no charter, and a ship that looks like an explosion in a girder factory...
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Amandin Adouin
Minmatar
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Posted - 2008.09.09 15:44:00 -
[7]
Please clarify that the chance for the car is constantly cycling through all the doors - so that the readers don't think, it can't be in the one I already opened, as it was empty before.
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Akita T
Caldari Navy Volunteer Task Force
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Posted - 2008.09.09 15:53:00 -
[8]
Yeah, I know the problem, but clarification is needed in order to have no misunderstandings and the proper answer.
a) the game show host always offers you the choice to switch (regardless of wether your initially picked door is a CAR or a GOAT)
b) the game show host always reveals a GOAT door
Of course, the game show host might try to tempt you to reverse your final decision or just give up entirely in exchange for some compensation, but that's out of the scope of this question.
_
SHOPS || Mission rewards revamp || better nanofix
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ReaperOfSly
Gallente
Lyrus Associates
The Star Fraction
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Posted - 2008.09.09 15:55:00 -
[9]
Originally by: Akita T
Yeah, I know the problem, but clarification is needed in order to have no misunderstandings and the proper answer.
a) the game show host always offers you the choice to switch (regardless of wether your initially picked door is a CAR or a GOAT)
b) the game show host always reveals a GOAT door
Of course, the game show host might try to tempt you to reverse your final decision or just give up entirely in exchange for some compensation, but that's out of the scope of this question.
Hehe, I didn't even notice he'd left those important bits out.
__________________________
Quote:
...bored, skint, no charter, and a ship that looks like an explosion in a girder factory...
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Sharra Savente
Domini Umbrus
Free Trade Zone.
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Posted - 2008.09.09 15:59:00 -
[10]
But I want the goat....
____
English doesn't borrow from other languages; it follows other languages down dark alleys, coshes 'em, then rummages in their pockets for loose bits of grammar. |
tiewan
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Posted - 2008.09.09 16:17:00 -
[11]
I don't want a car. You have to pay tax when you win a car, they cost a lot in insurance and gas and maintenance.
I will happily take a goat. One goat can keep your entire yard trimmed and fertilized.. no more yardwork!
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P'uck
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Posted - 2008.09.09 16:20:00 -
[12]
Originally by: Xtreem
The Monty Hall Paradox
hell yeah, i hate it.
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Int3r
Minmatar
Athena Enterprises
Caduceus Alliance
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Posted - 2008.09.09 16:29:00 -
[13]
As soon as the host reveals a door, there are 2 remaining doors to choose from. You can swap, meaning you get to pick again, this time from 2 doors. Chances are 50% now, so it shouldnt matter.
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Baldour Ngarr
Interwarp Plexus
Controlled Chaos
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Posted - 2008.09.09 17:35:00 -
[14]
Originally by: Int3r
As soon as the host reveals a door, there are 2 remaining doors to choose from. You can swap, meaning you get to pick again, this time from 2 doors. Chances are 50% now, so it shouldnt matter.
Most people will say this, and it's wrong.
When you pick a door, the host knows what is behind the other two doors. He will always pick one that doesn't have the car behind it.
Suppose you pick Door 1 to begin with. There are three possibilities, all equally likely:
The car's behind Door 1. No matter which door the host opens, you should not switch.
The car's behind Door 2. The host opens Door 3. You should switch.
The car's behind Door 3. The host opens Door 2. You should switch.
Ergo, there's a 2/3 chance you are better off by switching. Now, if someone walks into the room after the host has opened the empty box, and you ask him to guess, he does indeed have a 50/50 chance. He's only got two boxes to choose from. You, on the other hand, are still gambling on whether or not your original choice was correct. It was, and is, only 1/3 likely to be so.
________________________________________________
"I tried strip mining, but I lost, and it's cold flying around in space naked." |
Slade Trillgon
Siorai Iontach
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Posted - 2008.09.09 17:38:00 -
[15]
Didn't read th ethread so as to not ruin my answer.
At first you had a 33% chance to pick the car. Now you have a 50% chance no matter if you stay or pick the other door. So it depends how I am feeling that day.
If I am squirrely I switch.
If I am cautious I will go with my initial gut feeling.
Either way your chances are now 50% either way you go the way I see it.
Slade
Originally by: Crumplecorn
NerfBat is now known as the WaveMachine.
DesuSigs
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KingsGambit
Caldari Knights
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Posted - 2008.09.09 17:59:00 -
[16]
I think I posted this one on here a year or so ago. I must admit it took me a short time to understand the statistical reason for the answer but knowing the answer I can't understand how I first thought I was inititally correct Didn't Kevin Spacey also throw this to his class in '21'?
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ReaperOfSly
Gallente
Lyrus Associates
The Star Fraction
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Posted - 2008.09.09 18:06:00 -
[17]
Originally by: Slade Trillgon
Didn't read th ethread so as to not ruin my answer.
At first you had a 33% chance to pick the car. Now you have a 50% chance no matter if you stay or pick the other door. So it depends how I am feeling that day.
If I am squirrely I switch.
If I am cautious I will go with my initial gut feeling.
Either way your chances are now 50% either way you go the way I see it.
Slade
Hehehehe. You are SO wrong. (See my previous post)
__________________________
Quote:
...bored, skint, no charter, and a ship that looks like an explosion in a girder factory...
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CryoHead
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Posted - 2008.09.09 18:08:00 -
[18]
Edited by: CryoHead on 09/09/2008 18:09:28
Damn, I wrote a small prog and indeed you win about twice as many times when you pick the other one
I have to add that I didn't believe the changing tactic.
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Slade Trillgon
Siorai Iontach
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Posted - 2008.09.09 18:25:00 -
[19]
Edited by: Slade Trillgon on 09/09/2008 18:25:58
Originally by: ReaperOfSly
Originally by: Slade Trillgon
Didn't read th ethread so as to not ruin my answer.
At first you had a 33% chance to pick the car. Now you have a 50% chance no matter if you stay or pick the other door. So it depends how I am feeling that day.
If I am squirrely I switch.
If I am cautious I will go with my initial gut feeling.
Either way your chances are now 50% either way you go the way I see it.
Slade
Hehehehe. You are SO wrong. (See my previous post)
He wanted heat, but I will not be so hot in my response.
I said the first guess was at 33% odds. With the second chance, no matter if you stay with your original choice or decide to change, that decision is made at a 50% probability not a 33%. The second time around you have a 33% chance that staying will be rewarded or a 50% chance that switching would be rewarded. I see the logic with this type of question and I understand that my original guess was at 33% probabiltiy but one option was also eliminated, so even though the original choice was made at 33% the current potential for it to still be right is 50% of the current possibilities. So my answer was geared towards how I felt if this situation was to arise, so I can not be wrong unless the situation arises and I loose
Slade
Originally by: Crumplecorn
NerfBat is now known as the WaveMachine.
DesuSigs
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CryoHead
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Posted - 2008.09.09 18:28:00 -
[20]
If you switch and realize that you would have won if you didn't you will eat your hat no matter how much of a math genius you are "I was told I would have a better chance... omg... what now?"
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Baldour Ngarr
Interwarp Plexus
Controlled Chaos
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Posted - 2008.09.09 18:34:00 -
[21]
Originally by: Slade Trillgon
I said the first guess was at 33% odds. With the second chance, no matter if you stay with your original choice or decide to change, that decision is made at a 50% probability not a 33%.
Not so.
Think of it this way, and perhaps it'll become clear. When you make your original choice, you KNOW that at least one of the doors you did not pick has a goat behind it. When the host shows you a goat behind one of them .. nothing has changed.
________________________________________________
"I tried strip mining, but I lost, and it's cold flying around in space naked." |
Slade Trillgon
Siorai Iontach
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Posted - 2008.09.09 18:40:00 -
[22]
Originally by: Baldour Ngarr
Originally by: Slade Trillgon
I said the first guess was at 33% odds. With the second chance, no matter if you stay with your original choice or decide to change, that decision is made at a 50% probability not a 33%.
Not so.
Think of it this way, and perhaps it'll become clear. When you make your original choice, you KNOW that at least one of the doors you did not pick has a goat behind it. When the host shows you a goat behind one of them .. nothing has changed.
Except that the game has been reset, there are now to doors and your decision is to stay or to switch is based on a 50%. Two choices not 3. It is total seperate decision at that point. If you stay yes your original choice was made at a 33% probability, but if you switch now you have a 50% chance of being wrong . I would rather stick with the 33% chance of being wrong then the 50% chance of being worng
It is really a matter of which numbers you want to bank on.
Slade
Originally by: Crumplecorn
NerfBat is now known as the WaveMachine.
DesuSigs
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ReaperOfSly
Gallente
Lyrus Associates
The Star Fraction
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Posted - 2008.09.09 18:42:00 -
[23]
Originally by: Slade Trillgon
Originally by: Baldour Ngarr
Originally by: Slade Trillgon
I said the first guess was at 33% odds. With the second chance, no matter if you stay with your original choice or decide to change, that decision is made at a 50% probability not a 33%.
Not so.
Think of it this way, and perhaps it'll become clear. When you make your original choice, you KNOW that at least one of the doors you did not pick has a goat behind it. When the host shows you a goat behind one of them .. nothing has changed.
Except that the game has been reset, there are now to doors and your decision is to stay or to switch is based on a 50%. Two choices not 3. It is total seperate decision at that point. If you stay yes your original choice was made at a 33% probability, but if you switch now you have a 50% chance of being wrong . I would rather stick with the 33% chance of being wrong then the 50% chance of being worng
It is really a matter of which numbers you want to bank on.
Slade
I say again: you are SO wrong.
__________________________
Quote:
...bored, skint, no charter, and a ship that looks like an explosion in a girder factory...
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Baldour Ngarr
Interwarp Plexus
Controlled Chaos
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Posted - 2008.09.09 18:45:00 -
[24]
Originally by: Slade Trillgon
Except that the game has been reset
No. It hasn't. You knew when you chose that the two doors you ignored had at least one goat behind them, and you still know that. Nothing has changed, or reset, and the odds of your original decision being correct are still 1/3.
If in doubt, construct a small program that will actually run the scenario for you. If you never switch, you'll lose about 2/3 of the time.
________________________________________________
"I tried strip mining, but I lost, and it's cold flying around in space naked." |
Baldour Ngarr
Interwarp Plexus
Controlled Chaos
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Posted - 2008.09.09 18:49:00 -
[25]
YOU PICK DOOR ONE.
1/3 chance that the car is behind door one. Host might open either of the other two doors. You lose by switching.
1/3 chance that the car is behind door two. Host opens door three. You gain by switching.
1/3 chance that the car is behind door three. Host opens door two. You gain by switching.
YOU PICK DOOR TWO.
1/3 chance that the car is behind door two. Host might open either of the other two doors. You lose by switching.
1/3 chance that the car is behind door one. Host opens door three. You gain by switching.
1/3 chance that the car is behind door three. Host opens door one. You gain by switching.
YOU PICK DOOR THREE.
1/3 chance that the car is behind door three. Host might open either of the other two doors. You lose by switching.
1/3 chance that the car is behind door two. Host opens door one. You gain by switching.
1/3 chance that the car is behind door one. Host opens door two. You gain by switching.
________________________________________________
"I tried strip mining, but I lost, and it's cold flying around in space naked." |
DubanFP
Caldari
Out of Order
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Posted - 2008.09.09 18:59:00 -
[26]
Edited by: DubanFP on 09/09/2008 19:02:24
It's a bit counter-intuative but the op is correct. I'll try to explain why as best as i can.
At first there are 3 doors. You choose one and it has a 1/3 chance of being correct.
Side A(your original choice is correct)
1 chance in 3 "Ignore this for now"
Set B (your original choice is incorrect)
2 chances in 3
Each of the two choices in Set B have a 1/3 chance. The host now interferes with the equation by removing one of the incorrect doors in set B. This is the defining interference that affects the equation. Now the likelyhood of you choosing the correct door on your first try, Set A, is still 33%. Set A and B never change. So now what's left is Set B with only 1 door left is stuck with the rest of the 2/3 or 66.6% chance of being the winner.
The chances of your first attempt is always 1/3. The chances of everything else, which drops to 1 door with the interference, is 2/3. |
Mark Lucius
Kinetic Vector
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Posted - 2008.09.09 19:05:00 -
[27]
Keyword being 'switch(ing)'. |
Slade Trillgon
Siorai Iontach
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Posted - 2008.09.09 19:11:00 -
[28]
I never said you two were wrong I just said from my experiance, that I would stick with my original choice. That can not be a wrong answer to the OP's question of, do YOU change.
Statistically I know that the 1st choice has a 33% probibilty of being right and the second choice I have a 50% probability of being right if I change. So ultimately we are looking at only a 16% differance in probablitiy, not that large of a gap. I would kick myself more if I switched and lost then if I stayed and lost.
What about you two? 
This equates to 2/3 of the time I loose, but that does not make me wrong for saying I would choose to stick with my option. That does not guaretee that I will loose.
The second chance also gives 50% chance of being wrong if you switch and that is where I put significance, not that I now have a 50% chance of being right if I switch. My answers never claimed you two were wrong, I even said in my 1st post that if I was "feeling" a certain way that I would make a certain decision. So go one with your statistics, which I showed I understood, and I will stick with my choices.
When I take mulitple choice tests and I make an educated guess at a question that I am unsure of, and later on I realize that one of the potential answers in the previous question that I did not pick, has been officially eliminated, I do not go back and switch my answer just because stats now show I have a better chance to get it right if I switch it. That is as long as the wrong answer was not chosen to being with I learned this lesson becuase most of the time that I did change answers I ended up getting the question wrong and also typically switched it from the right answer 
Maybe I am the lucky guy that has the odds fall my way most of the time. That happens in stats sometimes. Got to love them.
Slade
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ReaperOfSly
Gallente
Lyrus Associates
The Star Fraction
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Posted - 2008.09.09 19:14:00 -
[29]
Edited by: ReaperOfSly on 09/09/2008 19:14:17
Originally by: Slade Trillgon
50%
This is where you're going wrong. There ARE no 50% chances here. Just get rid of the whole 50% thing from your mind.
__________________________
Quote:
...bored, skint, no charter, and a ship that looks like an explosion in a girder factory...
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DubanFP
Caldari
Out of Order
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Posted - 2008.09.09 19:15:00 -
[30]
Edited by: DubanFP on 09/09/2008 19:17:04
Originally by: Slade Trillgon
I would kick myself more if I switched and lost then if I stayed and lost.
You're saying that you would choose a 1/3 chance of winning over a 2/3 chance of winning? Then justify it by saying you would be annoyed if it was your first choice. Even though you know full well that changing would effectively double your likelyhood of winning? Your logic isn't.
Personally I would kick myself in the ass for making the stupid decision a lot more then for making the incorrect one.
_______________
"Cheap" and "Lame" are words created by people who refuse to admit they have been completely outclassed |
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