```On 7/17/05, Olaf Klischat <klischat / cs.tu-berlin.de> wrote:
> Graeme Defty <ruby_quizzer / yahoo.com> writes:
>
> > Sorry, all. New to the list. I accidentally posted my
> > previous under a nonsense user id :-)
> >
> >> > Unless I'm mistaken, in the 5e6-from-1e9 sampling,
> >> the probability
> >> > that a sampling contains exactly one number from a
> >> given 200-numbers
> >> > interval is 200.0*(1/200)*(199.0/200)**199 =
> >> 0.3688. The probability
> >> > that this happens for 20 such 200-numbers
> >> intervals is
> >> > 0.3688**20 = 2.1e-09.
> >>
> >> I think you are wrong. A rough estimates of this
> >> probability gives me
> >> 1e-2171438.
> >> Actually, it should be a bit smaller, but at least
> >> the order of
> >> magnitude of the order of magnitude is right :)
> >> Quite impressive...
> >>
> >> Paolo
> >>
> >>
> > I think he is wrong too (sorry. Missed the previous
> > post, so I don't know who it was)
>
> Me.
>
> > but I think I think
> > it's wrong for a different reason.
> >
> > I got the probability of getting exactly one number in
> > a specific interval to be as follows:
> > Probability of one *specific* number in the interval
> > 1/20
> > Probability of all the other 19 OUT of that interval
> > (19/20)**19
> > But we have 20 specific numbers to consider, so:
> > 20 * 1/20 * (19/20)**19
> > or
> > (19.0/20)**19
>
> Right, that's what I did too, but I was talking about a 200-numbers
> interval, not a 20-numbers one :)

It's wrong anyways. You both are assuming that all these events are
independent, and multiply their probability, but they are not. One
neat way to see this is remarking that you didn't use the fact that
the intervals are 5000000. If there were only one such interval (that
is, if you were doing an 1 out of 200 sampling), the probability would
have been obviously 1. If your formula were correct, I could apply it
to this case, obtaining a contradiction.

Paolo

```