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From: jlg@lanl.ARPA
Newsgroups: net.bio,net.origins,net.sci
Subject: Re: The missing step -- self-reproducing organisms
Message-ID: <16506@lanl.ARPA>
Date: Tue, 20-Nov-84 18:35:34 EST
Article-I.D.: lanl.16506
Posted: Tue Nov 20 18:35:34 1984
Date-Received: Thu, 22-Nov-84 06:50:23 EST
References: gatech.10770 <3469@ecsvax.UUCP> <10810@gatech.UUCP> <1262@hao.UUCP> <474@uwmacc.UUCP>
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Organization: Los Alamos National Laboratory
Lines: 32

> > 
> >    I think the concept that everyone is trying to get at here is this:
> > 
> > If an event has a probability of occuring that is greater than zero, and there
> > are an infinite number of attempts at it, then the probability that it will
> > eventually occur is indeed 1, no matter how small the probability that it will
> > happen on a given attempt. The only assumption needed here is that time
> > goes on forever (and I'm not going to debate that here, I take that as a given).
> 
> This argument is an example of the gambler's fallacy:  if I lose
> *this* time, then it's more likely I'll win *next* time.  The outcome
> of event i does not affect the outcome of event j in any way, for
> independent events.  (If the events are not independent, then the
> above argument doesn't apply anyway.)
> 
> The event could occur the first time; it might never occur.

Neither one of these are quite right (neither is really wrong either).
If the probability of an event is 'p' per try (0<p<1) then the probability
that the event will NOT occur in 'n' tries is:
                               n
                    q  =  (1-p)

The probability that the event will occur in the 'n' tries is '1-q'.  
The limit of 'q' as 'n' approaches infinity is clearly zero, so in an
infinite number of tries, the event has probability 1 of occuring.
However, at any given time that you check the experiment for results,
an infinite number of tries has not yet occured.  Therefore, the 
probability of success is not quite 1.  If the event has not occured 
at time 't' then future time evaluation must be done as if the counter
'n' were reset to zero at 't' - that's what the independence of trials
implies.