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But if I prepare an electron with say spin up, then measure it again for spin up I will detected spin up 100% of the time.

Also, if I prepare my electron in spin up, but rotate my equipment by 90 degrees the results will show that I only detect spin up with a probability of 0.5 Also, the measuring process will affect the electron and change it's state to the direction of detection.

Prepare my electron again in the spin up state, but this time rotate my equipment by an angle θ, I can work out the probability by Cos

^{2}θ/2

So for example, if my equipment was rotated to say 60 degrees, it would give a 75% probability of detecting spin up for an electron that was prepared in the spin up state.

Have I understood that properly?

Also, have all different angels been tested experimentally against their predicted probabilities? Do they all give the expected results compared to the predicted probability or are there some small angles, like say 10 degrees, where the probability is that near to 1 (0.9924 I think), experimentally it just shows 100%?