Thanks Bhobba. I think you had a better grasp of what I was actually asking (again, without the context of the previous replies in the thread this was actually posted, it seems to apply to a more general query as to "how are measurements taken" which is not at all what I was referring to.
I suspect PeterDonis is referring to more general cases as I already noted the statistical rationale. Also DrChinese seems to be even more general in terms of the "validity of scientific results" overall...
Neither of which are at all my actual question, which I do appreciate was not necessarily evident given it is no longer in the appropriate context of the thread following comments in which it was posted in response to.
Of course, if the mathematical formality predicts that a certain outcome will occur with a given probability, and sufficient repetition of experiments not only helps verify the theory/model, but also thereby reinforces that the experiment is conducted appropriately.
HOWEVER - my real point at heart was more in regards to the comments that allude to making measurements of AN ELECTRON (or whatever 'particle') at various stages throughout the experiment - there is, in my opinion, no reasonable means to identify that such an electron is indeed the exact same one (what does that even mean?)
EXAMPLE
If A theory of whatever suggests (for example) that 'particles' go from A through B and 50% result at C and 50% result at D and that separately one can identify the particle emission at A, then they can also be detected if required at B, then detectors at C and D agree precisely (when sufficient numbers have been involved), that there is a 50/50 disttribution between thee two --- Then any detection at C or D one can then claim, rightfully of course, that it has agreed with every step of the experiment and theory --- That's not what I was questioning.
When someone tries to create a scenario, then such as "what if we measure ... of the electron at B and then measure if that electron is at C or D" for example, WHEN there is some attempt to identify a specific single, individual electron - that is what I am having difficulty with and I suspect Bhobba appreciated that point, given the mention of being able to state it strictly.
The correlation mentioned by PeterDonis is exactly as I mentioned that statistical results.