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)