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From: friesen@psivax.UUCP (Stanley Friesen)
Newsgroups: net.bio,net.origins,net.sci
Subject: Re: The missing step -- self-reproducing organisms
Message-ID: <154@psivax.UUCP>
Date: Mon, 26-Nov-84 13:30:03 EST
Article-I.D.: psivax.154
Posted: Mon Nov 26 13:30:03 1984
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>> 
>>    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.
> -- 
> Paul DuBois		{allegra,ihnp4,seismo}!uwvax!uwmacc!dubois

I am sorry but the original statement *is* correct, it is *not* the
gamblers fallacy.  The confusion arises because it *sounds* like an
increase in probability is being invoked, when it is not.  It is true
that the outcome of event j doesn't affect the probability of event i,
but that has nothing to do with the limit as n approaches infinity of
P(at least one success in n trials), which is what the original statement
was talking about.  The mathematical result is that given any *finite*
sequence of trials there is a positive probability of 0 successes, but
that probability approaches 0 asymptotically as n approaches infinity.


My qualifcations in this area include a Master's Degree in Biostatistics.
					Stanley Friesen