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From: gwyn@Brl-Vld.ARPA
Newsgroups: net.physics
Subject: Re:  Coin Flips - (nf)
Message-ID: <1171@sri-arpa.UUCP>
Date: Thu, 24-May-84 11:21:53 EDT
Article-I.D.: sri-arpa.1171
Posted: Thu May 24 11:21:53 1984
Date-Received: Fri, 1-Jun-84 03:09:29 EDT
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From:      Doug Gwyn (VLD/VMB) <gwyn@Brl-Vld.ARPA>

The way I learned probability theory, probabilities are "conditional".
P(a|b) denotes the probability that a is true, given that one knows
that b is definitely true.  The usual laws of probability then are
	P((not a)|b) = 1 - P(a|b)	if "a or (not a)" is a tautology
	P((a or c)|b) = P(a|b) + P(c|b) - P((a and c)|b)
	P((a and c)|b) = P(a|c) * P(c|b)
If all terms in a given context end in "|b" then the "|b" is often
omitted, and assumed to be a condition in the environment.
Baye's theorem follows trivially from (a and c) == (c and a):
	P(c|a) = P(a|c) * P(c|b) / P(a|b)
And so forth.  The idea of conditional probability is a formalization
of the (obvious) fact that a probability assessment must be dependent
on one's state of knowledge of relevant factors.