[Koshkin]

I don’t think this is correct. The two particle system is prepared in a perfectly known state (e.g. both spins up). There’s nothing random about it. Randomness only occurs at the measuring device, if it not aligned with the direction of the spin of the incoming particle.

[zkmon]

Nope. They don't "have" their own state until one of them is measured. But they do have a correlated state which exists before measurement, which says they have opposite/same states. The individual states arise only after measurement. I'm not a physicist, but wrote a Quantum Simulator.