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I went through a paper last week about the Bell inequality and how it is incompatible with QM. Something along the lines of probability in classical regards being 1/3 but in quantum mechanics it is 1/4. It went into some basic principles of how this is determined through quantum entanglement to be 2 separate variables measured on 2 entangled particles. OK then. I file it away in the pile labeled "not fully understood". But then something doesn't sit right... wouldn't 2 variables with 2 possible values be 1/4 chance of any of the 4 possible "states" occurring? That's just classical probability.