[extropy-chat] what is probability?

[Rafal Smigrodzki]

On 1/16/07, gts <gts_2000 at yahoo.com> wrote:
> On Mon, 15 Jan 2007 18:44:23 -0500, Rafal Smigrodzki
> <rafal.smigrodzki at gmail.com> wrote:
>
> > ### I would see it this way: The meaning of "random" is "obeying the
> > principle of indifference, where the sample space is unambiguously
> > described". If the sample space is exactly two outcomes, then each one
> > must occur 50% of the time, or else the coin is weighted, and the
> > tosses are not quite random anymore.
>
> Hmm, I think this is not at all what is or should be the definition of
> "random".

### Yeah, I agree, I was to some extent being rhetorical :)

--------------
>
> As the word is normally defined, a series of tosses of an unfair coin
> still result in a completely random sequence! How can you suggest
> otherwise?

### Now, is that true? Let's say you have an unfair coin, which 99% of
the time drops heads  and only 1 % tails. Would you call the results
of tossing it a "completely random sequence"? What if the coin is only
slightly unfair, dropping 50.0001 % heads? Is the resulting sequence
random?

Note that any deviation from the principle of indifference allows a
player who knows about it to make arbitrarily large amounts of money
betting on the outcomes, given sufficiently long but finite series of
bets. The PI is a corollary of the Martin-Lof concept of randomness.

The PI is not in the definition of randomness, but any statistically
significant deviations from it in a sequence of events let you
conclude the events are not fully random.

Rafal