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[REBOL] Re: My Statistical Thoughts on Monty Hall Problem (non-REBOL)

From: bga:bug-br at: 20-Dec-2001 10:07

From: <[lgidding--aaa--allianz--com--au]>
> I think your logic might be flawed.....
LOL! :) No, it is not, I assure you.
> >Now, the other guy excluded 9998 doors and the second group only has one > >door now... But as we saw above, the probabitily that the prize is in
this
> >second group is 9999/10000. So the probability that the prize is in this > >single door is 9999/10000 and in the door you choose is 1/10000. That's > >why you *MUST* change to the other door. :) > > You appear to believe that the original 1/10,000 chance is still valid > after 9998 the doors have been opened.
And it *IS* valid. See the other analysis posted to this list.
> Surely like the coin which has no knowledge of its previous toss, > the odds have no knowledge of their previous length.
No no no no... This is the wrong way to think about it!
> For example: > > Imagine a Roulette wheel with 10000 numbers > I pick no 1 and have a 1/10000 chance > > The next time the wheel has reduced to 36 numbers > I still have no 1 but now I have a 1/36 chance > > Finally the wheel is reduced to just 2 numbers > I still have no 1 but now I have a 1/2 chance > > But my odds, if i swap to no 2, cannot possibly be improved > by my knowledge that 9998 PREVIOUSLY losing numbers > have now been dropped from the wheel.
The problem here is that you are ignoring the fact that the other guy told you about the 9998 no-prize entries and this is exactly what make this problem interesting! When 9998 numbers were excluded, you learned that they were not the correct ones (and they were part of the original problem). Initially you had 1/10000 chance of winning and that's why we can be pretty sure that you didn't and the prize is in the other group. Now, from the other group, all but *ONE* has been released as not having the prize... the prize can not move groups and it will still be on the second group (9999/10000 chance) and the chance the it is the first one you picked is 1/10000. -Bruno