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From: ram@zedat.fu-berlin.de (Stefan Ram)
Newsgroups: comp.misc
Subject: Re: Truly Random Numbers On A Quantum Computer??
Date: 30 Mar 2025 14:32:46 GMT
Organization: Stefan Ram
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Ethan Carter <ec1828@gmail.com> wrote or quoted:
>The definition of ``probability'' (in the sense of how to interpret it)
>is sort of an open problem. 

|The probability P(A|C) is interpreted as a measure of the
|tendency, or propensity, of the physical conditions describe
|by C to produce the result A. It differs logically from the
|older limit-frequency theory in that probability is
|interpreted, but not redefined or derived from anything more
|fundamental. It remains, mathematically, a fundamental
|undefined term.
"Quantum Mechanics" (1998) - Leslie E. Ballentine

>Thus far we have interpreted the probability of an event of a given
>experiment as being a measure of how frequently the event will occur
>when the experiment is con- tinually repeated.

|One of the oldest interpretations is the /limit frequency/
|interpretation. If the conditioning event /C/ can lead 
|to either A or "not A", and if in /n/ repetitions of such 
|a situation the event A occurs /m/ times, then it is asserted
|that P(A|C) = lim n-->oo (m/n). This provides not only 
|an interpretation of probability, but also a definition 
|of probability in terms of a numerical frequency ratio. 
|Hence the axioms of abstract probability theory can 
|be derived as theorems of the frequency theory. 
|
|In spite of its superficial appeal, the limit frequency
|interpretation has been widely discarded, primarily because
|there is no assurance that the above limit really exists for
|the actual sequences of events to which one wishes to apply
|probability theory.
|
"Quantum Mechanics" (1998) - Leslie E. Ballentine