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From: gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>)
Newsgroups: net.bio,net.origins,net.sci
Subject: Re: The missing step -- self-reproducing organisms
Message-ID: <5986@brl-tgr.ARPA>
Date: Wed, 21-Nov-84 09:47:53 EST
Article-I.D.: brl-tgr.5986
Posted: Wed Nov 21 09:47:53 1984
Date-Received: Fri, 23-Nov-84 03:04:51 EST
References: gatech.10770 <3469@ecsvax.UUCP> <10810@gatech.UUCP> <1262@hao.UUCP> <474@uwmacc.UUCP> <16506@lanl.ARPA>
Organization: Ballistic Research Lab
Lines: 16

The fallacy was in attempting to lump the concepts "has occurred during
the past N years" and "has a probability P of occurring in N years"
together to decide that P = 1.  Probability in its technical sense has
properties somewhat different from its everyday usage.

The attempt to estimate probabilities for rare events is fraught with
difficulty.  A recent example is the attampt to determine nuclear
reactor safety:  How does one estimate the probability of a specific
class of failure that has never yet been observed?  What are the odds
for a reactor having a catastrophic meltdown?  What are the odds of
a Three-Mile Island class disaster (1 has been observed in N reactor-
years; is the correct answer "1/N reactors per year"?)?

Sampling theory tells us that the relative error of a mean value
computed from N samples is 1/sqrt(N - 1).  When N is 0 or 1, what
is the expected error of the estimate?