wtf? Probability

[IronFist]

Ok, you know that puzzle where they say "if you have 3 doors and behind two of them are goats and behind the other one is a car," and then they have you pick a door, and then the host opens a door that you did not pick to reveal a goat and then asks you if you want to change your choice?

Well, some people said "yes, you should change your choice because then you have a 66% chance of being right."

Other people said "no, that's wrong. After he opens one of the goat doors, you have a 50% chance of being right because there are only two choices."

Now, to most people, that answer would make since. You have two doors. You're either going to get it right or you're not. 50/50, right?

Well, apparently not. This site explains why the 50/50 answer is wrong, and then if you don't believe them (like me), it gives you simulators to run that prove that by changing your guess you will win about 66% of the time.

What I don't get is how he says if there's room with 100 doors and you pick one and then he opens 98 doors to reveal goats and you switch your guess you have a 99% chance of getting it right. wtf???????????????????????

WTF???????

[_William_]

I think I will go hit my head on the wall now.

[joedoe]

It is pretty simple, if unintuitive.

When you pick a door, you chances are 1 in 3.

When the guy reveals a goat in one of the other doors, your chance on the door you originally picked is still 1 in 3.

However, if you swap your choice to the other door, the probability must make up the difference, which is 2 in 3.

The mistake most people make is that when one door is eliminated, they believe that the odds change to 1 in 2, which is incorrect because the original odds still apply. There are still 3 doors involved in the game.

[mickey]

Iron,

Go see a doctor. It's pretty obvious from this thread that your back is giving you great pain.

mickey

[IronFist]

I suddenly get it now. The tables on the first page explained it to me.

Crazy.

[PHILBERT]

I think its a load of crap. No matter what, your odds are always 50/50. You either get it right, or you don't get it right.

If you get AIDS, you have a 50/50 chance of getting a cure. You either get one, or you don't.

And I find it funny that out of 100, without changing my mind, I got 98 wins and 2 losses. I should go to Vegas with those odds.

[PHILBERT]

Oh now THIS IS even more bullcrap.

[FngSaiYuk]

Originally posted by PHILBERT
I think its a load of crap. No matter what, your odds are always 50/50. You either get it right, or you don't get it right.

If you get AIDS, you have a 50/50 chance of getting a cure. You either get one, or you don't.

And I find it funny that out of 100, without changing my mind, I got 98 wins and 2 losses. I should go to Vegas with those odds.

You're missing one important difference between basic probability and gaming theory. See, the game involves, say 100 doors to pick from. If they go through each door one at a time and the door they open is empty EACH time, AND the prize is NOT moved, AND you continue to get a chance to change your decision, the odds are NOT reset each time. You get a better chance of picking the correct door each time because you're eliminating all of the doors that have already been picked. The prize is going to be in ONE of the REMAINING doors.

[Ego_Extrodinaire]

there were no empty doors, there were goats. Do you get to keep it if you don't win the car??

[FngSaiYuk]

Originally posted by Ego_Extrodinaire
there were no empty doors, there were goats. Do you get to keep it if you don't win the car??

Yah yah, that... I'm used to prize/no-prize. As long as ya get the gist of my meanin'...

Edit:
Oh yah... Hi Blooming Lotus... your post style VERY much differs from Ego_Extrodinaire.

[joedoe]

Originally posted by Ego_Extrodinaire
there were no empty doors, there were goats. Do you get to keep it if you don't win the car??

Only if you promise not to molest them the way you normally do Ego

[Ego_Extrodinaire]

I don't want it then

[joedoe]

Ahahaha. You aren't so bad Ego

[YongChun]

http://www.cut-the-knot.org/peter.shtml
http://www.cut-the-knot.org/hall.shtml

[Meat Shake]

Goat?
Bah. Give me a sheep and some velcro gloves.