A fascinating mathematical problem

quote:

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Originally posted by Haroon:
John and Simon

Sorry to be boring you, but if you are happy that switching is right why come back to read the thread?

If you want other problems to solve why not start a NEW topic hey? Or is that too much of a problem for you to solve?

Look here i'm arguing my position out of interest and debate not because i have something personal agaist those who thinking switching is correct. If you find it tiresome thats up to you, you go and do something else and leave us be on this thread.

Im gonna stop here now because carrying on is useless when you get people resonding like you both have. I've put my views forward no one has actually explained why its wrong, just keep tellin' me another way and that pointless. I have tried to put my self in the view of the switching theory and found for me that it doesnt seem to work - explanation given in posts above. Now if you think my theories are wrong then why not try to actually explain to me why and how MY view is wrong rather than just telling me it is flawed.

Like I say now end of. Matthew thanks for at least trying to explain your position. As far as im concerned we can just put this aside.

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Haroon,
the host's choices are cg, gg, gc. By removing a goat he's left with c, g, or c.

You, on the other hand, still have g, g or c - your original 1/3 choice.

Now if you 'switch' to the SAME door you originally picked it can't suddenly have just g or c behind it, it MUST still have the original options g, g or c.

If you switch to the hosts 2nd door then it has either c, g or c behind it. ie you have 2/3 chance of finding the car.

But like I said before, if this isn't working for you, get your significant other to play host and see for yourself. Better yet, take up Matthews offer of £10K as if we're wrong and you're right then you can't possibly lose.

Haroon,

I find your arguments very difficult to follow so it is difficult to point out exactly where you are going wrong.

But, if i read you correctly, when you say...

"Let say we elim A
We chose C which had 1/3 chance
and A+B had 2/3 of car, but as explained above so to do A+C have 2/3 of car"

...you don't really have 2/3 of a chance as you are sticking with C whatever happens so the odds of A+C are irrelevant to your choice.

In contrast the switchers get to choose *both* A+B (2/3) and then decide which one they really want *after* the host has told them which of A or B has a goat.

Your argument requries that we transfer probability to your choice after you have made it -- which would mean that is you just got the host to reveal goats behind both doors this would transfer a 100% probability to your original choice was and you'd always get the car.

Matthew

ok, looking at this:

A+B = A+C = 2/3;
A=0,
B=C

for starters you missed out B+C which also = 2/3
A+B = A+C = B+C = 2/3
if a=0 then continuing with this logic
B = C = B+C = 2/3

so now you've got an obvious problem.

What actually happens is that you pick C = 1/3 and the host then picks A+B = 2/3.
He then eliminates (A OR B). So you still have C=1/3 and he STILL has A OR B = 2/3. What you don't have is A+C or B+C because you've only picked 1 door. You get A+C or B+C by switching doors. If you switch to the SAME door then you would have C+C but we know that's not a valid option.

Difficult one to fathom. I've been swayed by both sides, but have decided the sensible thing to do is switch.

Either your chances go up or stay the same, they don't go down.

Or is there a 3rd arm to this discussion?

Kevin I like your thinking

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

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

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