A statistical question

  • Thread starter Villan Of The North
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Villan Of The North

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The following is part of a post in another thread and it reminded me of one of my favourite statistical problems. I'd love to know what Heath and others think about it

HeathfieldRoad1874 - 11/6/2014 17:43

LOL. My Degree and Masters Degree are in Statistics. Don't try and bullshit me about Probabilities. The more you flip a coin, the odds stay the same. 50-50.
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So what's your take on the Monty Hall problem. I just love how this works and it's been proven and yet still, top statistical theorists can't agree 100% why despite the problem being so simple.

 
Is that the one where if you change your mind after one being illuminated then your odds increase over those of sticking with your original choice??

If it is, then I'm sure there was a proof of sorts. I'd have to look it up to be sure.
 
Here's a page that offers the chance to try it for yourself.

Enjoy, and we'll try and explain it after a few have had a go.

http://math.ucsd.edu/~crypto/Monty/monty.html
 
I've seen the explanation before, it kind of makes sense but it breaks some rules that should be unbreakable where a certain percentage of the posdibilities just "disapears" and as you know yourself, the total of the proabilities should always add up to 100%. As I understand it it's this concept, of disappearing probability, that causes all the discussion, the theory itself is quite easy to prove.
 
It depends on the exact conditions of the experiment, which sometimes do change, but yes, the proof revolves around all probabilities adding up to 1.

Some of the difficulty revolves around the fact that Monty knows what's behind each door.

I hope people try the test first, then we can go through the Maths later.
 
Just tried it 10 times switching every time and 10 times sticking with the same door.

Switching: 8 out of 10 wins
Sticking: 5 out of 10 wins
 
McGrath4Pope - 11/6/2014 23:37

Just tried it 10 times switching every time and 10 times sticking with the same door.

Switching: 8 out of 10 wins
Sticking: 5 out of 10 wins
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That's not bad. the higher the sample, the closer you'll get to 33/67.

interesting, isn't it.
 
I seen a very good documentary on this subject a few years ago - I think it is on youtube somewhere, I will see if I can remember the title and post it up.
 
This is a rather amusing demonstration of the principle and a reasonably explained theory of how the statistics work.

[youtube=tvODuUMLLgM&feature=youtube_gdata_player]
 
Pretty good VOTN, I watched one by Dan Ariely but I cant find it. Its begining to bug me because I wouldnt mind watching it again.
 
HeathfieldRoad1874 - 12/6/2014 08:38

McGrath4Pope - 11/6/2014 23:37

Just tried it 10 times switching every time and 10 times sticking with the same door.

Switching: 8 out of 10 wins
Sticking: 5 out of 10 wins
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That's not bad. the higher the sample, the closer you'll get to 33/67.

interesting, isn't it.
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It is, I've come across this before but won't pretend to truly understand it.

Would this principle be true in 'Deal or No Deal' when the opportunity to swap the box comes up? Or is it irrelevant as, supposedly, no one knows what is in each box and therefore the others have been removed purely by chance as opposed to the Monty Hall problem where doors are 'removed' based upon prior knowledge?
 
Is it time for an answer on how it works?

It's quite simple really. When you select the first door, you have a 1 in 3 chance of getting it right. That never changes. As the total probabilities must add up to 1, the other 2 doors have a 2 in 3 chance of being right. The fact that one is taken away, and the person taking it away knows what's behind it and takes a goat, doesn't change these odds.

Effectively, every choice apart from the door you've selected has a 2 in 3 chance, so the odds are in favour of changing.
 
Derren brown explained this best a while ago. when you have three doors in front of you your guese is 1 out of three that you will get it right. the one door is revealed showing a goat. This then leaves two doors. one with a goat and one with a car. now this doesnt make it a 50/50 choice.... there is still a 1 in 3 chance your right but the possibility that you will won goes up by 33% because one of the original choices has been eliminated
 
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