mbs
No, Carrol's right. Although I'm not a number cruncher, it's quite clear that the probability of getting the non-white ball (or rolling a five) is far greater if you perform the experiment many times. Think of it this way: someone who plays the lottery often for the entirety of their life is more likely to win at some point (even though their odds don't increase with each succesive failure) than another person who buys a single ticket.
-- Luke
--On Wednesday, September 19, 2001 8:49 PM -0400 Max Sawicky <sawicky at bellatlantic.net> wrote:
> I don't think so. YOu're thinking of an experiment
> that would go like this -- a very large urn has a
> million balls in it, all but one white. If you
> draw all the balls, obviously one of them will
> be white. But if you draw and replace, then in
> each draw your chances of coming up white are
> still one in a million. So your premise depends
> on the trials being dependent on each other. Each
> null result increases the likelihood of a non-null
> result subsequently. So it depends on exactly what
> we're talking about, which I have forgotten.
>
> mbs
>
>
> Yes. This is tricky, but probability, as I understand it, is not really
> a matter of prediction. So what we are talking about is a situation not
> before the millionth & one roll of the dice but _after_ all 1 million
> and one rolls have occurred, and we know the results of NONE of the
> rolls. What is the probability that when we open the record books to
> check on what has happened that someplace in that record a roll of five
> has occurred.
>
> Carrol