Bell's inequality refuted via elementary algebra

[FrediFizzx]

It's a great slogan:

"Quantum mechanics is about real probability factors for real physical events"!

Real probability factors are what I would call "irreducible randomness".

Hmm... randomness that we can't reduce. I don't think probability factors are always necessarily about randomness. They can simply be about the lack of knowledge about certain processes.
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Ah ha well that I think is the interesting question.

Lack of knowledge <-> hidden variables
Irreducible randomness <-> something new and shocking to physics and even incompatible with our inborn cognitive abilities (spooky!)

Lack of knowledge doesn't necessarily imply hidden variables. We don't know exactly what happens when a photon interacts with an electron but we know there is a probability factor of the square root of the fine structure constant involved. Particle physics is full of things like this. Most of the probability factors were deduced from scattering experiments.
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[Mikko]

Lack of knowledge doesn't necessarily imply hidden variables. We don't know exactly what happens when a photon interacts with an electron but we know there is a probability factor of the square root of the fine structure constant involved. Particle physics is full of things like this. Most of the probability factors were deduced from scattering experiments.
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Lack of knowledge means that there is something unknown. This unknown can be called, in absence of better knowledge, a "hidden variable".

[FrediFizzx]

Lack of knowledge doesn't necessarily imply hidden variables. We don't know exactly what happens when a photon interacts with an electron but we know there is a probability factor of the square root of the fine structure constant involved. Particle physics is full of things like this. Most of the probability factors were deduced from scattering experiments.
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Lack of knowledge means that there is something unknown. This unknown can be called, in absence of better knowledge, a "hidden variable".

Well... what would be the "hidden" variable then when a photon interacts with an electron? And... don't tell me we don't know because it is hidden. Take a stab at what it might be.