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proof of Bell's theorem (quantum physics)

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Assume we have some source of electrons with entangled spins. This means that if A and B are a pair, if I choose to measure them both in the same axis, one will be up and other down.  Now, A and B are sent off to two boxes very far from each other, which we will call Trump and Biden. Trump and Biden can each measure the spin of their electron in three different axes. These are the 3 axes and we choose them so that they are 120 degrees apart from each other. When A arrives at Trump, Trump randomly chooses an axis to measure A's spin in, and Biden does the same thing with B. But they do it independently from each other, so Trump could measure spin around 2 and Biden around 3, for example. If the boxes measure their electron to be spinning, then they flash red, or if it spins down they flash white. Someone notes if they're the same colour or not. This experiment has been repeated many times. The question is, what fraction