I was wondering just what physical properties of an electron influence it's probability of being detected in a certain spin state? For example, if I prepare an electron in the spin up state along say the way y axis (vertical axis) and pass it through a detector that is at 0 degrees, then using the formula Cos2θ/2, I know there is 100% probability of detecting spin up. If I rotate my detection device to say 90 degrees then I know there is 50% chance of my equipment detecting spin up and if I rotate my device to say 60 degrees then I know there is a 75% chance of detecting a spin up. But what is it exactly (if known) about the electron that leads to these probabilities? Why does an angle of 60 degrees lead to a 75% probability of detection? By the way I have no background in physics at all, sorry. I'm just a very interested layman and my math isn't great either!