Roger Mills put finger to keyboard:
That logic is flawed. Sure, you've got two boxes left, one which holds the car and one which doesn't, which is where you're getting your 50/50 from.
But the host opening a box skews it, because if one of the remaining boxes contains the car he *has* to open the other one.
Or people trying both to prove it, which I reckon is the real reason.
There must also be a sizeable number (as this thread has demonstrated) that believe there is no benefit in switching.
Not all of it. Proofs are human constructs.
An analogy might be the difference between beauty and poetry written about beautiful things.
Alex
Uh? They are trying to win a CAR! I know everyone in the US has already got three, but still.
Human discoveries - at least all the ones we know about.
In maths, the "poetry" *is* the beautiful thing.
You have to be *very* careful with the wording of the problem: see
for an explanation (also for a couple of other readily confusing problems)
Yes, indeed. That was my initial stance - and it took a lot of shifting
- but I'm now reluctantly accepting that the switchers are right. In the unlikely event that I was a contestant, I would certainly have believed that there was no benefit prior to the thorough airing given to the subject in this thread.
Indeed, and its understandable since on the surface it seems like a simple probability based problem, whereas its actually a probability and information theory based problem - where the injection of a small bit of extra information skews the odds.
It is an inference problem where the key evidence is clearly presented but the correct interpretation requires a *VERY* clear head.
Appealing to common sense fails dismally...
There's a pschological trick too, in that only those that switch don;t just their own previous judgment, as only those that think they made the wrong choice will choose to switch. Leaving you will an oppd stat that the more single minded person or teh purpose that believs they arte always rioght won't switch.
It's a 1/3 chance if you stick with your original choice - you started at
1/3 and all that has happened is a 100% certainty that a losing door will be opened [1]. If you want to make it 50-50 toss a coin to decide which of the final doors to open. [1] And it's not random which door is opened by the host unless you chose the winning door (giving him a choice of two to open).
hich is the winner, thus the odds are now 0.5 for each door. Thus it makes no difference whether one switches doors or not. Statistical probability fi gures are nothing more than reflections of the data they're based on, and o pening one door changes the available data. Missing that point is where so many are going wrong.
ammed into it - the output is merely a reflection of the views of the progr ammer.
t establish it to be true, everyone makes mistakes. It seems to be a popula r myth that high IQ and specialist subject knowledge immunise people from t hat.
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