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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In Loving Memory of SatanWantsMe 2006-2008
SWM Wiki | Journal | What I am listening to right now
SWM Wiki | Journal | What I am listening to right now
What sex is the goat?
"I started out with nothin' and I still got most of it left" - Seasick Steve
I know what Aegis's Answer would be 
Nobby wrote:
What sex is the goat?
They don't know, when the goat filled out his papers, for "Sex" he wrote "Yes".
Can't sleep, clown will eat me.
Yes, you have 2/3 chance of picking a goat first time around and when he reveals the other goat you win by changing
You should switch. Doing so gains you a a two thirds probability of winning.
People round here are far too smart 
Switch doors if you want a 2 in 3 chance of winning the car was the correct answer.
Switch doors if you want a 2 in 3 chance of winning the car was the correct answer.
In Loving Memory of SatanWantsMe 2006-2008
SWM Wiki | Journal | What I am listening to right now
SWM Wiki | Journal | What I am listening to right now
Allegory wrote:
You should switch. Doing so gains you a a two thirds probability of winning.
How does that work?
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.
Can't sleep, clown will eat me.
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
In Loving Memory of SatanWantsMe 2006-2008
SWM Wiki | Journal | What I am listening to right now
SWM Wiki | Journal | What I am listening to right now
Always switch doors unless you have "faith" in your door.
Just as Planned.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Edit: better formatting
Edited, Mar 31st 2008 7:28pm by Timelordwho
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
Just as Planned.
Ok. I get it now.
Can't sleep, clown will eat me.
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
In Loving Memory of SatanWantsMe 2006-2008
SWM Wiki | Journal | What I am listening to right now
SWM Wiki | Journal | What I am listening to right now
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)
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)
Love,
PunkFloyd
PunkFloyd
Quote:
then you know that must be the right choice.
a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.
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
Nyan nyan
Nyan nyan
Nihao
Goujasu derishasu ekaruchaa
Bringing derailâ„¢ back.
Qui s'estime petit deviendra grand.
Qui s'estime petit deviendra grand.
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
Nyan nyan
Nyan nyan
Nihao
Goujasu derishasu ekaruchaa
No this is awesomer
click
In Loving Memory of SatanWantsMe 2006-2008
SWM Wiki | Journal | What I am listening to right now
SWM Wiki | Journal | What I am listening to right now
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.
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.
Just as Planned.
Baron von tarv wrote:
Quote:
then you know that must be the right choice.
a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.
Math says to **** off
SWM wrote:
That link contains perhaps my favorite viewer comment ever:
Quote:
this is gay like your dad cause i sucked your mom's tits
Totally ought to be a meme.
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