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Scholar

5,085 posts

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?

Should You? Why?

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

Ministry of Silly Cnuts

19,519 posts

What *** is the goat?

"I started out with nothin' and I still got most of it left" - Seasick Steve

Scholar

8,619 posts

I know what Aegis's Answer would be

Jarkeld Hammerhiem Lvl 36 Paladin/Lvl 30 Armourer

Lestril Hammerhiem Lvl 40 Monk/Lvl 28 Provisioner Blackburrow server

Iaedian Tailchaser lvl 60 Fury/36 Jeweler. Proud member of <Bane> Crushbone server

Your mind is like a Parachute, it only works if it's open.

Worst. Title. Ever!

17,092 posts

Nobby wrote:

What *** is the goat?

They don't know, when the goat filled out his papers, for "***" he wrote "Yes".

Can't sleep, clown will eat me.

Scholar

2,122 posts

Yes, you have 2/3 chance of picking a goat first time around and when he reveals the other goat you win by changing

Belkira the Tulip wrote:

While I do tend to agree with Planks

This spot is no longer devoted to anyone in particular.

Repressed Memories

20,963 posts

You should switch. Doing so gains you a a two thirds probability of winning.

Scholar

5,085 posts

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

2,189 posts

Allegory wrote:

You should switch. Doing so gains you a a two thirds probability of winning.

How does that work?

Viseziox wrote:

I think you're a forum ****

Fancy Shmancy Wiki

[ffxisig]186182[/ffxisig]

Worst. Title. Ever!

17,092 posts

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.

Scholar

5,085 posts

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

Unplanned

13,235 posts

Always switch doors unless you have "*faith*" in your door.

Just as Planned.

Repressed Memories

20,963 posts

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.

Scholar

424 posts

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.

2,189 posts

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.

Viseziox wrote:

I think you're a forum ****

Fancy Shmancy Wiki

[ffxisig]186182[/ffxisig]

Repressed Memories

20,963 posts

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.

Unplanned

13,235 posts

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

Just as Planned.

Worst. Title. Ever!

17,092 posts

Ok. I get it now.

Can't sleep, clown will eat me.

Repressed Memories

20,963 posts

This video may help a few of those who are still confused; it makes a lot of sense.

Scholar

5,085 posts

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

4,900 posts

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)

PunkFloyd

Scholar

8,619 posts

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.

Jarkeld Hammerhiem Lvl 36 Paladin/Lvl 30 Armourer

Lestril Hammerhiem Lvl 40 Monk/Lvl 28 Provisioner Blackburrow server

Iaedian Tailchaser lvl 60 Fury/36 Jeweler. Proud member of <Bane> Crushbone server

Your mind is like a Parachute, it only works if it's open.

Wants you as a new recruit!

17,414 posts

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

derail™ back.

Qui s'estime petit deviendra grand.

Bringing Qui s'estime petit deviendra grand.

Scholar

5,085 posts

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

Unplanned

13,235 posts

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

Just as Planned.

Scholar

2,122 posts

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

Belkira the Tulip wrote:

While I do tend to agree with Planks

This spot is no longer devoted to anyone in particular.

Your Wet Nightmare

19,727 posts

SWM wrote:

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.

**B***i*__U__~~S~~
Smileys

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