Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site psivax.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxj!ihnp4!zehntel!tektronix!hplabs!sdcrdcf!psivax!friesen 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 Date-Received: Thu, 29-Nov-84 03:42:55 EST References: gatech.10770 <3469@ecsvax.UUCP> <10810@gatech.UUCP> <1262@hao.UUCP> <474@uwmacc.UUCP> Organization: Pacesetter Systems Inc., Sylmar, CA Lines: 33 Xref: sdcrdcf net.bio:140 net.origins:571 net.sci:246 >> >> 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