adding probabilities
in [Math]
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From: Predictor on 13 Mar 2005 11:43 Given no more information than provided in your original message, one can only infer that the probability of A, by either mechanism is "at least 0.9". The other information needed is the relationship between mechanisms 1 and 2 (their "correlation"). It is possible that mechanism 2 only causes event A when mechanism 1 already has, which would result in a probability of 0.9. If it is the case that mechanism 2 generates event A in all cases when mechnism 1 does not, then the probability is 1.0. If the outcome of mechanisms 1 and 2 are uncorrelated, then the formula you derived is correct, although it is usually re-arranged algebraically as (using your notation): P1 + P2 - (P1 * P2) -Will Dwinnell http://will.dwinnell.com
From: packat on 26 Mar 2005 11:32
Predictor wrote: > Given no more information than provided in your original > message, one > can only infer that the probability of A, by either > mechanism is "at > least 0.9". > > The other information needed is the relationship between > mechanisms 1 > and 2 (their "correlation"). It is possible that > mechanism 2 only > causes event A when mechanism 1 already has, which would > result in a > probability of 0.9. > > If it is the case that mechanism 2 generates event A in > all cases when > mechnism 1 does not, then the probability is 1.0. > > If the outcome of mechanisms 1 and 2 are uncorrelated, > then the > formula you derived is correct, although it is usually > re-arranged > algebraically as (using your notation): > > P1 + P2 - (P1 * P2) > In a more general situation, please search Google for Dempster-Shaeffer theory. pac > > -Will Dwinnell > http://will.dwinnell.com |