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#1 Mar 31 2008 at 2:45 PM Rating: Good
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You're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door and the host, who knows what's behind the doors, opens another door and reveals a goat - no matter what you have picked he will always reveal a goat. He then says to you "Do you want to switch?"

Should You? Why?
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#2 Mar 31 2008 at 2:49 PM Rating: Excellent
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What *** is the goat?
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#3 Mar 31 2008 at 2:50 PM Rating: Good
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I know what Aegis's Answer would be Smiley: sly
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#4 Mar 31 2008 at 2:51 PM Rating: Good
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Nobby wrote:
What *** is the goat?


They don't know, when the goat filled out his papers, for "***" he wrote "Yes".
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#5 Mar 31 2008 at 2:58 PM Rating: Good
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Yes, you have 2/3 chance of picking a goat first time around and when he reveals the other goat you win by changing
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#6 Mar 31 2008 at 2:58 PM Rating: Good
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You should switch. Doing so gains you a a two thirds probability of winning.
#7 Mar 31 2008 at 3:06 PM Rating: Decent
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People round here are far too smart Smiley: frown

Switch doors if you want a 2 in 3 chance of winning the car was the correct answer.
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#8 Mar 31 2008 at 3:06 PM Rating: Good
Allegory wrote:
You should switch. Doing so gains you a a two thirds probability of winning.

How does that work? Smiley: dubious
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#9 Mar 31 2008 at 3:07 PM Rating: Good
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Allegory wrote:
You should switch. Doing so gains you a a two thirds probability of winning.


Exactly how though?

I understand that you have a 67% chance of picking a goat the first time, and a 50% chance of picking a goat the second time if you repick. But in reality, him revealing one of the goats has no way of changing what is actually behind the first door you chose. (This isn't a cat in a box).

It's like if a teacher asked a question, which you had no clue what the answer was. Multiple choice, A, B, or C. You pick A at random, and the teacher tells you afterwards that C is not the correct answer. You don't gain anything really by changing your answer after that.
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#10 Mar 31 2008 at 3:12 PM Rating: Decent
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TirithRR the Mundane wrote:
It's like if a teacher asked a question, which you had no clue what the answer was. Multiple choice, A, B, or C. You pick A at random, and the teacher tells you afterwards that C is not the correct answer. You don't gain anything really by changing your answer after that.


But you should change your answer...

You have a 1 in 3 chance of your first answer being correct, which means that the other 2 answers combined have a 2 in 3 chance of being correct.

If the teacher always tells you that one of the answers you didnt choose is incorrect and tells you which one it is then you have 2 choices i) stick with your original which has a 1 in 3 chance of being correct or ii) switch to the other remaining answer which now has a 2 in 3 chance of being correct.

Switch TirithRR, you know it makes sense
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#11 Mar 31 2008 at 3:15 PM Rating: Good
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Always switch doors unless you have "faith" in your door.
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#12 Mar 31 2008 at 3:16 PM Rating: Good
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To make the situation more apparent imagine that instead of 3 doors you have 100 doors.

You pick any door with a 99% chance of being wrong. The host then reveals every door remaining except one to have a goat. There are now two doors remaining, the one you picked with a 99% chance of being wrong and one unknown. This door has 1-.99 probability of being a goat, 1%. Therefore you should switch.
#13 Mar 31 2008 at 3:18 PM Rating: Good
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If you want the car, you should switch.

The reason why it works is simple: There's 2 possibilities, on your first random pick you either pick the car 1/3 of the time, or a goat 2/3 of the time.

If you randomly pick the car, then the other goat is out of the picture and you lose by switching, meaning you lose 1/3 of the time.

If you randomly pick the goat, then the other goat is once again out of the picture, but by changing you pick the car, therefore winning 2/3 of the time.
#14 Mar 31 2008 at 3:18 PM Rating: Excellent
Allegory wrote:
To make the situation more apparent imagine that instead of 3 doors you have 100 doors.

You pick any door with a 99% chance of being wrong. The host then reveals every door remaining except one to have a goat. There are now two doors remaining, the one you picked with a 99% chance of being wrong and one unknown. This door has 1-.99 probability of being a goat, 1%. Therefore you should switch.

This makes no sense to me.. no matter HOW many doors are eliminated, there's 2 left, and each have an equal opportunity of being a goat... meaning that no matter what you do it's 50/50 when you're left with 2...

Or maybe i'm missing something. Smiley: glare
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#15 Mar 31 2008 at 3:26 PM Rating: Excellent
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It's only 50% if you don't include the information about the previous doors.

Out of 100 doors any door you pick is almost certainly the wrong door. If you know you're wrong, and he takes away all other choices except one, then you know that must be the right choice.

Or you can try thinking of it this way. Instead of the doors you can actually see all the prizes. You can see which of the 99 are goats and which one is a car. Pick any prize at random (not caring what you win). Most of the time you will pick a goat, because there are 99 of them and only one car, after switching you would have ended up with a car. If you by chance pick the 1 car out of those 99 goats then after switching you would have picked a goat. So since you pick a goat most of the time, by switching you end up picking a car most of the time.
#16 Mar 31 2008 at 3:27 PM Rating: Excellent
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Because the door you picked has a higher probability of being a goat door than a car door. 1/3 probability to 2/3 probability, easy decision.


Perhaps a graphical interpretation will help.

O is car, X is goat. Always pick door #1 (for convenience sake). If you want to pick other doors, result is the same, it just requires 9 diagrams.

 
pick door #1, door 2 is revealed as goat. swap to door 3.  
sorry, screwed by probability this round. 
[o] [x] [x] 
pick door #1, door 3 is revealed as goat. swap to door 2, winnar! 
[x] [o] [x] 
pick door #1, door 2 is revealed as goat. swap to door 3, winnar! 
[x] [x] [o] 


Edit: better formatting

Edited, Mar 31st 2008 7:28pm by Timelordwho
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#17 Mar 31 2008 at 3:40 PM Rating: Good
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Ok. I get it now.
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#18 Mar 31 2008 at 3:42 PM Rating: Decent
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This video may help a few of those who are still confused; it makes a lot of sense.
#19 Mar 31 2008 at 3:45 PM Rating: Decent
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Allegory wrote:
This video may help a few of those who are still confused; it makes a lot of sense.


Thanks, that certainly clears thing up Smiley: smile
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#20 Mar 31 2008 at 3:47 PM Rating: Good
Always switch.

Your initial pick is correct 1/3 of the time. (Random system)

After the host eliminates one of the doors, switching effectively gives you a 2/3 chance of winning. (Non-random system)
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#21 Mar 31 2008 at 3:47 PM Rating: Decent
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Quote:
then you know that must be the right choice.
No you don't, it's Equally as likely that you picked the right door the first time.

a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.
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#22 Mar 31 2008 at 3:51 PM Rating: Good
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SWM wrote:
Allegory wrote:
This video may help a few of those who are still confused; it makes a lot of sense.


Thanks, that certainly clears thing up Smiley: smile
This is the most awesome video...

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#23 Mar 31 2008 at 3:54 PM Rating: Decent
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Sogoro the Malevolent wrote:
SWM wrote:
Allegory wrote:
This video may help a few of those who are still confused; it makes a lot of sense.


Thanks, that certainly clears thing up Smiley: smile
This is the most awesome video...

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No this is awesomer

click
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#24 Mar 31 2008 at 3:56 PM Rating: Excellent
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Quote:
No you don't, it's Equally as likely that you picked the right door the first time.

a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.


Read my post and you'll see why this is incorrect.

When you pick a door, you have a 1/3 chance of being right, AND (now here is the important part) a 2/3 chance of being wrong. You don't get a 50/50 shot anywhere. If you still can't get it, allegory's video gave a very informative description.
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#25 Mar 31 2008 at 3:57 PM Rating: Good
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Baron von tarv wrote:
Quote:
then you know that must be the right choice.
No you don't, it's Equally as likely that you picked the right door the first time.

a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.

Math says to **** off
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#26 Mar 31 2008 at 3:57 PM Rating: Excellent
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SWM wrote:
Sogoro the Malevolent wrote:
SWM wrote:
Allegory wrote:
This video may help a few of those who are still confused; it makes a lot of sense.


Thanks, that certainly clears thing up Smiley: smile
This is the most awesome video...

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No this is awesomer

click


That link contains perhaps my favorite viewer comment ever:

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this is *** like your dad cause i sucked your mom's tits


Totally ought to be a meme.
#27 Mar 31 2008 at 4:00 PM Rating: Excellent
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The continuing saga of the Allakhazam office.
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#28 Mar 31 2008 at 4:17 PM Rating: Good
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Timelordwho wrote:
The continuing saga of the Allakhazam office.
Smiley: nod

Edited, Mar 31st 2008 8:21pm by Sogoro
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#29 Mar 31 2008 at 5:08 PM Rating: Good
SWM wrote:
Sogoro the Malevolent wrote:
SWM wrote:
Allegory wrote:
This video may help a few of those who are still confused; it makes a lot of sense.


Thanks, that certainly clears thing up Smiley: smile
This is the most awesome video...

Nyan nyan
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No this is awesomer

click

Superior Lulz
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#30 Mar 31 2008 at 5:13 PM Rating: Decent
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Math says to @#%^ off
Read the fUcking post you muppet.

I am not arguing that you shouldn't pick the other one you think cnut, i am pointing out that when left with two boxes it is not automaticly a 100% result when switching.

2 boxes left, only one has a car thus 50/50. the fact you have shortened the odds doesn't make it as was stated
Quote:
you know that must be the right choice.
It's PROBABLY the right choice, but you CANNOT be certain.

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#31 Mar 31 2008 at 5:27 PM Rating: Good
Baron von tarv wrote:
Quote:
Math says to @#%^ off
Read the fUcking post you muppet.

I am not arguing that you shouldn't pick the other one you think cnut, i am pointing out that when left with two boxes it is not automaticly a 100% result when switching.

2 boxes left, only one has a car thus 50/50. the fact you have shortened the odds doesn't make it as was stated
Quote:
you know that must be the right choice.
It's PROBABLY the right choice, but you CANNOT be certain.



With two doors to choose from, your odds are 50/50 only in a _random_ system.

But when you are posed with your second choice (to switch or not), it is not a random system: one door will win 1/3 of the time and the other will win 2/3 of the time. This is, by definition, not random.
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#32 Mar 31 2008 at 5:30 PM Rating: Decent
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But when you are posed with your second choice (to switch or not), it is not a random system: one door will win 1/3 of the time and the other will win 2/3 of the time. This is, by definition, not random.
Still not 100% Smiley: schooled
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#33 Mar 31 2008 at 5:32 PM Rating: Excellent
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Baron von tarv wrote:
Quote:
But when you are posed with your second choice (to switch or not), it is not a random system: one door will win 1/3 of the time and the other will win 2/3 of the time. This is, by definition, not random.
Still not 100% Smiley: schooled


You're such a f*cking moron. It's really funny.
#34 Mar 31 2008 at 5:34 PM Rating: Decent
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You're such a f*cking moron. It's really funny.
Please explain how ANYTHING i have said is incorrect.

Go on try.

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#35 Mar 31 2008 at 5:45 PM Rating: Good
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Incidentally, this is nothing like how Deal or No Deal works.
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#36 Mar 31 2008 at 5:48 PM Rating: Good
Baron von tarv wrote:
Quote:
But when you are posed with your second choice (to switch or not), it is not a random system: one door will win 1/3 of the time and the other will win 2/3 of the time. This is, by definition, not random.
Still not 100% Smiley: schooled


Exactly, I never said you had a 100% chance.

Baron von tarv wrote:

2 boxes left, only one has a car thus 50/50.


Your statement is 100% incorrect. Smiley: schooled
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#37 Mar 31 2008 at 5:50 PM Rating: Good
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it's dead AND alive... or something?
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#38 Mar 31 2008 at 6:22 PM Rating: Good
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Baron von tarv wrote:
2 boxes left, only one has a car thus 50/50. the fact you have shortened the odds doesn't make it as was stated
Quote:
you know that must be the right choice.
It's PROBABLY the right choice, but you CANNOT be certain.

I was trying to avoid tautology; it would be redundant to reiterate such a pleonasm.^^ Obviously the entire situation still involves probability.

Your statement about 50% is still incorrect.

Edited, Mar 31st 2008 9:27pm by Allegory
#39 Mar 31 2008 at 11:01 PM Rating: Decent
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Baron von tarv wrote:
Please explain how ANYTHING i have said is incorrect.

Go on try.



This bit is wrong

Quote:
2 boxes left, only one has a car thus 50/50.


The box you chose was chosen at random from 3 boxes thus a 1 in 3 chance of winning. The box that is left was not left unopened randomly, it was left unopened on the basis that the other box contained a goat and so the probability of it containing the car is the sum total of the boxes at the initial point of the game (1 in 3 plus 1 in 3 = 2 in 3).
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#40 Apr 01 2008 at 1:41 AM Rating: Decent
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The box you chose was chosen at random from 3 boxes thus a 1 in 3 chance of winning. The box that is left was not left unopened randomly, it was left unopened on the basis that the other box contained a goat and so the probability of it containing the car is the sum total of the boxes at the initial point of the game (1 in 3 plus 1 in 3 = 2 in 3).
Jesus people try reading for a change.

There is a 66% chance your CHOISE of box is correct, there is a 50% chance that the car is in a particular box.

the point i am making is no matter how much you swing the chance your CHOICE is correct because there is still two boxes left you can't be certain that you have the right box.
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#41 Apr 01 2008 at 1:56 AM Rating: Decent
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Tarv your original statement was:
Quote:
No you don't, it's Equally as likely that you picked the right door the first time.

a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.

It's not equally as likely that you picked the right door the first time. It's not a 50% chance of one being right.

I don't mean to be rude, but what your trying to arguing what you are saying is pointless. You're now arguing that you mean that out of the two boxes/doors there is a 50% chance one has a car and that one can't be certain which box/door has the car. While both of these statements are true they mean nothing useful. Out of any two objects you have a 50% chance of selecting one, and nearly every situation involving probability lacks perfect certainty. Right, but not relevant.

Edited, Apr 1st 2008 4:58am by Allegory
#42 Apr 01 2008 at 2:54 AM Rating: Excellent
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Allegory wrote:
It's not equally as likely that you picked the right door the first time. It's not a 50% chance of one being right.
It is if you just take a snapshot in time, which is what Tarv's doing. Technically, you're right. But once you eliminate one door and then forget it existed, you're left with 2 choices. At this point, you're first guess has as likely a chance of winning as changing does.

Personally, I like to look at it the other way around. The doors I didn't pick, have a 2/3 chance of being wrong and after opening the third door, it increases the likelihood that the remaining door I didn't pick, is still wrong. In case none of you notice, I like to bend things so they work for me, because I'm never wrong.
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#43 Apr 01 2008 at 3:34 AM Rating: Good
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#44 Apr 01 2008 at 3:57 AM Rating: Decent
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Did you also have pets named Dylan, Dougal and Zebedee?
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#45 Apr 01 2008 at 6:32 AM Rating: Good
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Sogoro the Malevolent wrote:
Timelordwho wrote:
The continuing saga of the Allakhazam office.
Smiley: nod

Edited, Mar 31st 2008 8:21pm by Sogoro


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#46 Apr 01 2008 at 6:40 AM Rating: Good
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I don't think this game sounds awesome.

But then, I'm not a big fan of "Deal or No Deal."
#47 Apr 01 2008 at 6:54 AM Rating: Excellent
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From The Straight Dope:

Cecil wrote:
A friend of mine did suggest another way of thinking about the problem that may help clarify things. Suppose we have the three doors again, one concealing the prize. You pick door #1. Now you're offered this choice: open door #1, or open door #2 and door #3. In the latter case you keep the prize if it's behind either door. You'd rather have a two-in-three shot at the prize than one-in-three, wouldn't you? If you think about it, the original problem offers you basically the same choice. Monty is saying in effect: you can keep your one door or you can have the other two doors, one of which (a non-prize door) I'll open for you. Still don't get it? Then at least have the sense to keep quiet about it.


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#48 Apr 01 2008 at 10:59 AM Rating: Decent
Uglysasquatch, Mercenary Major wrote:
Allegory wrote:
It's not equally as likely that you picked the right door the first time. It's not a 50% chance of one being right.
It is if you just take a snapshot in time, which is what Tarv's doing. Technically, you're right. But once you eliminate one door and then forget it existed, you're left with 2 choices. At this point, you're first guess has as likely a chance of winning as changing does.


Even if viewed as a snapshot in time, it's not a 50% chance. Nowhere in this particular example did you ever have a 50% chance of being right.

You can only make the claim that you've got a 50% chance if car is randomly behind one of two curtains. The point is that the car is not randomly behind the curtains. There is a 1/3 chance it's behind the curtain you originally picked and a 2/3 chance of being behind the other curtain. This is, by definition, not random so you do not have a 50% chance.

As an analogy, think of flipping a loaded coin.






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#49 Apr 01 2008 at 11:01 AM Rating: Decent
I take it someone watched 21.

I think the reasoning was ********* and you now have a 50/50 of winning with either door.
#50 Apr 01 2008 at 11:03 AM Rating: Good
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PunkFloyd the Flatulent wrote:
Even if viewed as a snapshot in time, it's not a 50% chance. Nowhere in this particular example did you ever have a 50% chance of being right.

You can only make the claim that you've got a 50% chance if car is randomly behind one of two curtains. The point is that the car is not randomly behind the curtains. There is a 1/3 chance it's behind the curtain you originally picked and a 2/3 chance of being behind the other curtain. This is, by definition, not random so you do not have a 50% chance.

As an analogy, think of flipping a loaded coin.


Ok, now you're being as dense as Tarv was. If you forget (should I bold that again or would you miss it again?) that there were 3 doors after one is opened, you only have 2 doors left. At this point, you do have a 50/50 shot. Taking the bigger picture, you never do. But, using the snapshot in time, where the 3rd no longer exists, you do have a 50/50 chance.
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#51 Apr 01 2008 at 11:30 AM Rating: Decent
Uglysasquatch, Mercenary Major wrote:
PunkFloyd the Flatulent wrote:
Even if viewed as a snapshot in time, it's not a 50% chance. Nowhere in this particular example did you ever have a 50% chance of being right.

You can only make the claim that you've got a 50% chance if car is randomly behind one of two curtains. The point is that the car is not randomly behind the curtains. There is a 1/3 chance it's behind the curtain you originally picked and a 2/3 chance of being behind the other curtain. This is, by definition, not random so you do not have a 50% chance.

As an analogy, think of flipping a loaded coin.


Ok, now you're being as dense as Tarv was. If you forget (should I bold that again or would you miss it again?) that there were 3 doors after one is opened, you only have 2 doors left. At this point, you do have a 50/50 shot. Taking the bigger picture, you never do. But, using the snapshot in time, where the 3rd no longer exists, you do have a 50/50 chance.


I am not being dense, this is exactly my point. You do *not* have a 50/50 chance. You have a 33.3/66.6 chance.

You only have a 50/50 chance if the car is randomly behind one of the two curtains, but it is not randomly behind one of the curtains. It's twice as likely to be behind the curtain not initially picked.
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