'Obvious' is in the eye of the beholder. Apart from that, mankind did not evolve with much statistical genes, so I agree with your warning.
R. E. Boss -----Oorspronkelijk bericht----- Van: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Namens Boyko Bantchev Verzonden: zondag 3 september 2006 20:22 Aan: Programming forum Onderwerp: Re: [Jprogramming] The Monty Hall Problem On 9/3/06, bill lam <[EMAIL PROTECTED]> wrote: > R.E. Boss wrote: > > Another way to see the obvious solution: suppose there are 100 doors, you > > pick one and the game master opens 98 of the others, all revealing goats, do > > you stick or switch? > > Thank you! This does make it obvious. `Obvious'? The only obvious thing here, IMO, is how misleading our intuition can be. This reminds me of a joke I was told many years ago. A mathematics professor, in the course of presenting a lecture: `From this it is obvious that ... [makes a pause] ... but is it obvious?' Then he makes a much longer pause and concludes, saying `Yes, it is indeed obvious'. In my experience, nothing is obvious in chance calculation problems, at least until one enumerates all possibilities and takes account of the dependencies between them (more or less like Oleg did for this particular problem). Intuition is too often deceptive in this kind of problems, and should never be relied upon. There is a curious phenomenon about probability problems. Often there are several ways to reason about a particular one, but (also often) some are wrong. And the difficult thing is not to grasp a correct proof when you read it (or to construct such a proof yourself). Somehow it is harder to tell why an incorrect but plausible proof really fails. Consequently, if you are presented with two contradicting `proofs', it may be difficult to tell which one is corect. Regards, Boyko ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
