A fascinating mathematical problem

Posted by: Minky on 18 April 2004

I've just finished reading "The curious incident of the dog in the night-time" by Mark Haddon. The book has a brief passage on something called "The Monty Hall" problem. Marilyn vos Savant, the smartest person in the world by virtue of her Guinness record IQ, was asked the following question (my words) :

In a game show there are three doors. Behind two of them are goats. Behind the third is a car. You are a contestant trying to win the car. You choose a door and the game show host opens one of the two remaining doors to reveal a goat. Which door is most likely to have the car behind it (should you stick or switch) ?

If you have never encountered this problem before, have a think about it.

When Marilyn vos Savant gave her answer she was quite soundly chastised by some very heavy-hitting brainiacs, and this is at least as fascinating as the problem itself, because (as I have also found) this baby seems to have an almost supernatural ability to turn otherwise mild-mannered people into red-eyed monsters Mad
Posted on: 21 April 2004 by Haroon
Kevin I like your thinking Wink

Guys seeing as my hteory is that it doesnt matter whether you stick or switch, Im gonna switch just to keep you happy Big Grin
Posted on: 22 April 2004 by Don Atkinson
Haroon,

Guys seeing as my hteory is that it doesnt matter whether you stick or switch, Im gonna switch

sensible move - under the circumstances

Cheers

Don
Posted on: 22 April 2004 by Don Atkinson
Haroon,

It is very difficult to follow your way of thinking-through this problem; and it is therefore very difficult to find a clear explanation of where and why your thinking is flawed.

I apreciate that you (and many others reading this thread) find OUR (ie the Switchers) logic completely baffling, and probably irritating. You are in good company - quite a few professors of mathematics came to similar conclusions to yourself when presented with this problem. Of course they were also wrong and I find thas quite disturbing

This is one of the beauties of this particular teaser. It really does make you have to think.

In my opinion, a big part of the problem is that the story-line is ALWAYS so very badly worded.

If (BIG IF) if it was made absolutely clear that the rules of the show were fully spelt out to each contestant BEFORE starting the game, that would help. If these rules made it clear that the host KNOWS where the car is, that would help. If the rules made it clear that the host would always open ONE of the two UNSELECTED doors AND always reveal a goat in doing so, that would help. If the rules made it clear the contestant ALWAYS has a chance to "change his mind", that would help.

More people would see the reason for switching, under these circumstances.

THEN we could move on to consider whether the probabilities would change under different rules, eg the Host has no idea of where the car is etc etc.

I can't see any easy way of helping you come to terms with this teaser and I can't see how to axplain where YOUR explanations are flawed.

However, it MIGHT help if you tried two things

1. Consider the problem assuming the contest is run with (say) 10 doors, or 5 doors, rather than 3 doors.

2. Get your partner to set up a dummy show (using 3 doors) where YOU act as the game-show host (so you know there is no cheating) and run a trial of (say) 100 shows, 50 where your partner sticks and 50 where your parner changes mind. Matthew and others might complain that a run of 50 isn't large enough, and they are right, but it should show a trend....

Hope this helps

Cheers

Don