> --- Carrol Cox <cbcox at ilstu.edu> wrote: >
> >
> > Max Sawicky wrote:
> > >
> > > Incidentally, in probability theory, an event with probability
> > > X is no more likely after one trillion trials than after
> > > the first one, assuming what happens in a trial does not
> > > depend on what has happened in previous ones. Put another
> > > way, if the chance of rolling a five is one in six, after
> > > a million rolls, it is still one in six, even if your
> > > first million rolls came up six.
>
> Hrrrmmmm .... When I quit this lark and open a casino, I promise
> there'll be
> free drinks for you night and day, Max, as long as you promise to
> stand by the
> roulette wheel and tell people that. Rolling a million sixes is
> pretty good
> evidence that a process which you thought was random, wasn't.
>
Actually, this is probably the only time I'll ever say this: Max is quite correct. The previous million rolls have no outcome on the fate of the next roll. Why? Well, because the chance of throwing 1 six is, unsuprisingly 1/6 (1 in 6). To do it twice is (1/6)^2, or 1/6*6 or 1/36. To roll a million consecutive sixes then is (1/6)^1 000 000. However, the next roll is still 1/6. The probability of getting 1 000 001 rolls of six in a row is (1/36)^1 000 001, but what we need to take into consideration is that you've already "used" (ie beaten the odds) on the first 1 000 000 throws. I hope I explained that OK... ;-/
Cheers
Zak