Ned Batchelder wrote:
> You aren't agreeing because you are arguing about different things.
> Thomas is talking about the relative probability of sequences of digits.
There is no such thing as “relative probability”, except perhaps in popular-
scientific material and bad translations. You might mean relative
_frequency_, but I was not talking about that specifically.
> Chris is talking about the probability of a single digit never appearing
> in the output.
I do not think that what I am talking about and what you think Chris is
talking about are different things.
> Thomas: let's say I generate streams of N digits drawn randomly from 0-9.
> I then consider the probability of a zero *never appearing once* in my
> stream. Let's call that P(N)
In probability theory, it is called the probability P(E) of the event E that
in n trials the probability variable X never assumes the value 0, which can
be defined as
P(E), E = {e_i | n ∈ ℕ \ {0}, i = 1, …, n} \ {X ≠ 0}, Ω = {1, 2, …, 9}
where the e_i are the singular events, or outcomes, of the probabilistic
experiment, and Ω is the sample space of the e_i.
> Do you agree that as N increases, P(N) decreases?
I do not agree that P(E), as defined above, decreases as n increases.
See also: <http://rationalwiki.org/wiki/Gambler%27s_fallacy>
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