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[psychnurse]

Stick with the bike... Its cheaper and you know you will get fitter  

 

  



Ta matey  

oh - and welcome back stranger  

[Banjax]

It was a clever explanation. But I maintain that opening the first door had no effect on what is behind the remaining 2. All that has happened is you have changed the chance from 1/3 to 1/2 by doing that because they are independant.

Let's say the game is tossing coins and you need 3 heads in a row.

1st go - your chance of winning is 2³ (2 outcomes to the power of 3 goes) of winning. 1/8.

2nd go. 2 throws left. Your chance has changed. 2². 1/4.

Last go. At this point you win with a head or loose with a tail. 50% chance. The previous turns have no effect on the spinning coin . The physics is the same whether the game was 3 in a row or just 1 go. The chance of you winning the game at this point is still 1/2.

It's the same with the doors. It essentially became a new game. When you choose, you simply face 2 doors. 1/2.

I have been reading up on this and it appears that we could both be right.

If the game show host knows where the bikes are (so always shows a bike - not the car) the chance is 2/3 for changing and Bannjaxx &STMO123 are right.

If the host doesnt know, the chance is 1/2. Presumably because 1/3 of the time he removes the car...

Try this. Use a big number of games - I used 2,000.
http://math.ucsd.edu/~anistat/chi-an/MonteHallParadox.html

the host does know - cos he'll ALWAYS show you the bike  

nice link btw

[jereboam]

This is the famous Monty Hall Problem - it's been around for many years but surfaced again a few years back when it was featured in a very interesting book called The Curious Incident of the Dog in the Night-time.

The maths that indicates that you should always change is impeccable, but the result is counter-intuitive, and I have problems accepting the conclusion.  So do many others.

If you want something else to think about, try and explain why the moon appears to be much larger when it has just risen.  But don't ask me for an expalnation - I don't know.

[Bandit127]

This is the famous Monty Hall Problem - it's been around for many years but surfaced again a few years back when it was featured in a very interesting book called The Curious Incident of the Dog in the Night-time.

The maths that indicates that you should always change is impeccable, but the result is counter-intuitive, and I have problems accepting the conclusion.  So do many others.

If you want something else to think about, try and explain why the moon appears to be much larger when it has just risen.  But don't ask me for an expalnation - I don't know.

The Monty Hall Problem still has my brain fairly busy as it happens. So I just Googled it.

I have learned that measurements of the moon show that it isn't  actually any larger whn it has just risen. And the often stated cause of refraction in the atmosphere would actually make it appear smaller verically.

Hmmm.

[STMO123]

This is the famous Monty Hall Problem - it's been around for many years but surfaced again a few years back when it was featured in a very interesting book called The Curious Incident of the Dog in the Night-time[/i].

The maths that indicates that you should always change is impeccable, but the result is counter-intuitive, and I have problems accepting the conclusion.  So do many others.

If you want something else to think about, try and explain why the moon appears to be much larger when it has just risen.  But don't ask me for an expalnation - I don't know.

Excellent book. I have a son with aspergers so was very interested in it. However, I find it somewhat strange that it was written by someone who doesn't have aspergers, but has such an insight into it.