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Awesome Game ShowFollow

#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...

Nyan nyan
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Goujasu derishasu ekaruchaa


No this is awesomer

click
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#24 Mar 31 2008 at 3:56 PM Rating: Excellent
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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...

Nyan nyan
Nyan nyan
Nihao
Goujasu derishasu ekaruchaa


No this is awesomer

click


That link contains perhaps my favorite viewer comment ever:

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


Totally ought to be a meme.
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