Are probabilities always and necessarily positive-definite?

I'm asking this because there is a thread, started by Dirac
and Feynman, saying the only difference between the classical 
and quantum cases is that in the former we assume the probabilities 
are positive-definite.

Thus, speaking of MWI, we could also ask: what is the joint 
probability of finding ourselves in a universe alpha and of 
finding ourselves in a universe beta, which is 180 degrees 
out of phase with the first one (whatever that could mean)?

s.

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