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Topic:
Probabilities not in [0,1]?
Replies:
8
Last Post:
Mar 12, 2013 10:56 PM




Re: Probabilities not in [0,1]?
Posted:
Mar 11, 2013 3:27 PM


On Mar 10, 8:36 pm, "Peter Percival" <peterxperci...@hotmail.com> wrote: > Is there a theory of probability in which probabilities do not lie in the > real interval [0,1]? More specifically, is there one in which the "space" > of probabilities may have points x, y, z with x < y, x < z but y and z not > necessarily comparable? > >  > Using Opera's revolutionary email client:http://www.opera.com/mail/
Yes for the first question , not that I know of for the second one .
More specifically , you can have negative probabilities and over unitary probabilities , as long as all the experimentally observable probabilities are between 0 and 1 .
Imagine you have two socks hidden in two drawers , set up for an experiment : The socks can be black or white in color .
You can ask only one of three questions : Is the sock in drawer 1 white ? Is the sock in drawer 2 white ? Are the socks in drawers 1 and 2 of different colors ?
And for any of those questions ,you wold get an answer 'yes' 100% of the time . How do we model this? We have four possible configurations corresponding to four probabilities : (white, white)> p1 (black,black) > p2 (black,white) > p3 (white,black) > p4
p1 + p2 + p3 + p4 = 1 (total probability) p3 + p4 = 1 (the socks are always different) p1 + p4 = 1 (the socks in the first drawer are always white) p1 + p3 = 1 (the socks in the second drawer are always white)
We obtain : (white, white)> 1/2 (black,black) > 1/2 (black,white) > 1/2 (white,black) > 1/2
This might seem absurd , but experiments to which this model is applicable are conducted in quantum mechanics . http://en.wikipedia.org/wiki/Bell%27s_theorem#Bell_inequalities http://en.wikipedia.org/wiki/Negative_probability http://en.wikipedia.org/wiki/Wigner_quasiprobability_distribution



