> > > Here's a math puzzle that's a lot easier to solve than it might seem at first. Can anyone do it?
> > >
> > > A number p is picked (by someone else) at random from a uniform distribution on the interval (0,1). Then a coin is crafted which, when tossed, results in heads with probability p and tails with probability 1-p. The coin is given to us without us being told what p is, and we have no way of deducing any additional information on the value of p besides experimentation.
> > >
> > > Given what we know, and since the problem's symmetric with respect to heads/tails, the chance of getting a heads is 1/2 on the first flip. I.e., we're 50% confident of getting heads when we're just about to make the first flip.
> > >
> > > The question is this: if we keep flipping the coin and getting heads, after which flip do we become 99% confident (or higher) that the next flip will also be heads?
> >
> > The trick I used was...
>
> [eighty-four paragraphs about math snipped]
>
> Uh... yeah. "A lot easier to solve than it might seem." Sure.
>
> -Faux "You sort of lost me after 'The trick I used was...'" Pas.

Well, the problem was really more targeted towards people who have had classes in probability/statistics and would understand what "uniform distributions" and "independent events" are, since I know quite a few such people read the forum. I wasn't writing it for the general audience (many of whom would have been lost just reading the question). So if you got lost that early, it didn't apply to you anyway.

I stand by the claim that it was easier than it might seem. There was one reciprocal, one subtraction, and that's it. Not only did it yield the answer, but it gave a *simple* and more general formula.