gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (12/26/85)
Thanks, Bill! It is important to realize that all "probability" measures are actually CONDITIONAL probabilities, dependent on the information available. In some contexts, there is a common condition, which may then be suppressed so that probabilities appear to be absolute measures. However, changed circumstances may require re-introducing the suppressed condition. For people who have never heard this before: P(A|B) is used to denote "probability of A, given B" where A and B are events. For example, one of the elementary probability formulae is: P(A and B | C) = P(A|BC) P(B|C) which, assuming the common context C, may be written P(A and B) = P(A|B) P(B) Assuming events A and B are statistically independent, then P(A|BC) = P(A|C) or, given C: P(A|B) = P(A) so one often sees the formula P(A and B) = P(A) P(B) But there are two assumptions buried in this. The moral is, beware of applying formulae when you don't fully understand the conditions under which they are valid.