My friends and I got into an argument about determinism, and I brought up that quantum events are random. But I couldn't prove it.

I found the Wikipedia page on "Bell's theorem", which seems to imply what I'm trying to show, because it disqualifying local hidden variable models. But I don't understand how the experiment works. I think I understand the steps taken:

1. An electron-positron pair is produced, with opposite spins.
2. Alice measures the spin of the electron along the x-axis.
3. Bob measures the spin of the positron along some axis, which could be the x-axis.
4. Alice and Bob compare their results, recording a +1 if their spins match, and a -1 if they do not.
5. A graph of "angle between Alice and Bob's axes" vs. "sum of many trials" is created.

The part I don't get is: Why would local hidden variable theories predict a triangular pattern for the graph, and likewise, why would entanglement predict a cosine?

My friends and I got into an argument about determinism, and I brought up that quantum events are random. But I couldn't prove it.

I found the Wikipedia page on Bell's theorem, which seems to imply what I'm trying to show, because it disqualifying local hidden variable models. But I don't understand how the experiment works. I think I understand the steps taken:

1. An electron-positron pair is produced, with opposite spins.
2. Alice measures the spin of the electron along the x-axis.
3. Bob measures the spin of the positron along some axis, which could be the x-axis.
4. Alice and Bob compare their results, recording a +1 if their spins match, and a -1 if they do not.
5. A graph of "angle between Alice and Bob's axes" vs. "sum of many trials" is created.

The part I don't get is: Why would local hidden variable theories predict a triangular pattern for the graph, and likewise, why would entanglement predict a cosine?