The Monty Hall problem

[nickeye]

It goes like this:

Imagine you're on "Let's Make a Deal". There are three doors in front of you. Behind one of the doors is A NEW CAR. Behind the other two are goats.
For those of us who may think otherwise (Sheep), the object is to get the car.

You pick a door. Monty Hall then opens up one of the OTHER two doors and shows a goat behind it (he knows where the car is; no matter what, he's not going to open that one). He then tells you that, if you want to, you can switch from your door to the other one that's still closed.

The question for you:
Do you switch doors, stick with your original pick, or, statistically, does it not matter?

Be careful; it's not what you think. Unless, of course, you think the right answer, in which case it IS what you think.

--NickEye

[MANdrew]

you have to switch



sig pic in 48 hrs

<img src="http://dxixrxt.20megsfree.com/mandrew1.JPG">

[furie]

goats aren't the same
species as sheep.




<img src="http://www.geocities.com/furie1335/wtcguy.jpg">

[nickeye]

goats aren't the same
species as sheep.
Yeah, you're right. That would just be sick. What was I thinking?

--NickEye

[reeshy]

I'd stick with the goat!

<img src=http://www.ripcat.free-online.co.uk/waitsgraphics/brshot.jpg>
Maybe me?

[furie]

I'd stick with the goat!


I bet you would, slugger



<img src="http://www.geocities.com/furie1335/wtcguy.jpg">

[Chet]

Yup, Goat's is good eatin'.

<img src= http://chet-young.8m.com/images/chet_young21.jpg>

[Sheeplovr]

Id be happy with a sheep wouldnt you?



number 333 its the way to be
http://members.hometown.aol.com/_ht_a/walrus701/images/breadsig.jpg
POWER AND CHAOS

[nickeye]

Oh, yeah; this one was a real winner. Guess I should've called it "What do you think about sex with goats?"

For anyone who cares, you should switch doors. There's a 1-in-3 chance that the car is behind your door, and 2-in-3 that it's behind the other door.

Crappy thread. I'm going to go work on my skills in the minors (i.e. the Word Association Game).

--NickEye

[HordeKing1]

NICKEYE - Let me begin by saying that math is not my forte. The hardes course I ever took was statistical psychology in undergrad. (Harder than all other undergrad, grad and law school course). I only got a B in it (fucked up my GPS) but I was actually happy with the B.

Anyway, I thought your answer was correct at first. When I began to second guess myself I asked my wife, an actuary and math teacher, and she said that switching won't improve your odds.

She checked with a statistician friendwho concurred. It makes sense to me, and I hope I can convey the concept as I understand it.

When you choose at first the odds are 1 in 3. When one choice is elimiated, it can ONLY be one or the other. The odds are 1 in 2 that you're choice will be correct whether you switch or not.

Eliminating one possibility doesn't increase the odds from 1/3 to 1/2. It's as if the original equation had never existed and the odds with the new equation are the same whether or not you switch.

http://members.aol.com/rnfpantera/hking2

[Big Jim]

I would take the $1200 he always offers you before you make the decision, and pass the two remaining doors to the lady with the purple face in a giant grape costume.

Happy Holidays from myself and all of us at 'NSYNC<img src = "http://publish.hometown.aol.com/jimandbryan/myhomepage/jimsigpic2.jpg?mtbrand=AOL_US"> Thanks MANdrew for this pic
SEEEEEYUH!!
*BIG JIM*

This message was edited by Big Jim on 12-19-01 @ 4:14 AM

[nickeye]

HK-

As much as I'd hate to disagree with the Horde Queen (pronounce that carefully), that's the answer that makes this question interesting (but, apparently, only to me). Math people tend to reduce it to 50-50 and get it wrong more than anyone.

See, the fact that Monty CAN'T open the door with the car changes things.

Picture this: instead of 3, there are 100 doors. You still pick one. Monty has to open 98 of the other doors and show only goats, leaving yours and one other still closed. Do you switch? If you don't, the only way you'd get the car is if you picked it on the first try (1-in-100). There's a 99-in-100 chance that you didn't pick it on the first try, and there's only one of those unpicked doors still closed. Same thing with 3 doors, except less intuitive.

I first read this question in "Ask Marilyn"; there was a ton of debate about it. Curious to hear what your wife thinks.

--NickEye

[Koala]

I shall try to explain the famous monty hall probability question. When you pick the first door you have a 1/3 chance of picking the right door. The odds on THAT door does not go to 1/2 chance once he shows you one of the doors. The other door is the one you would want to pick.
Just because there are 2 possible outcomes does NOT mean you necessarily have a 50-50 chance. For ex. If soemone was to take a shot from half court, he either will make the shot or he won't. There are 2 possible outcomes. Those 2 outcomes are not equally likely to occur. I would bet that he would not make it.
Another example would be: take a deck of cards. pick a card. what is the probability that you would get the queen of hearts? 1/52. If I then turned over 50 cards from the deck to show you that they are not the queen of hearts and left one that wasn't turned over, that card that I didn't show you has a much better chance of being the queen of hearts than the one you originally you picked.

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[HordeKing1]

Now you know why math isn't my forte.

I do not understand how a 1 in 2 chance will be anything more or less than that. I don't get the connection to the other part of the equation. Even if the odds were 1 in 50 and 48 are eliminated, there can be only 2 choices.

Given 2 choices, and knowing that it can be only one or the other, it seems to me that the odds are 50/50.

The basketball analogy doesn't make sense as there are other factors involved, namely the skill of the player, his or her fatigue, level of stress, distractions, etc. In our example it must be one or the other.

Next you'll tell me that when you multiply fractions you end up with less than you started before. I mean 1/2 x 1/2 = 1/4! No way!

http://members.aol.com/rnfpantera/hking2

[MANdrew]

like i said in the first reply...you have to switch...
(note the quiet confidence in that statement)




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You too can have a MANdrew made sig pic...just ask nicely

[nickeye]

I guess this is the perfect forum to prove the point. I'm going to pick a number between 1 and 50 and e-mail it to Sheeplovr (just because he's a consistent reader and impartial judge). The first one to reply to this thread with a number between 1 and 50 gets to switch to the unopened door after we're done. The Horde King has to pick a number and not switch.

If the first person to reply gets it right after switching, he wins. If HK gets it right without switching, he wins.

Someone pick...

[Sheeplovr]

i know something that you dont know i know somthign u dont know

number 333 its the way to be
http://members.hometown.aol.com/_ht_a/walrus701/images/breadsig.jpg
POWER AND CHAOS

[HordeKing1]

That's not analagous. Eliminate 48 cards and guarante mine is one of the two remaining - that's the test.

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