Yep. And to answer the question about randomness - it's absolutely vital to have a good source of noise to obscure the underlying pattern to prevent the secret information leaking - but the mathematical part that manipulates that noise into the encrypted output has to be precise. That's the distinction made here relating to probability.

Disclaimer: Not a crypto expert. Just like reading about it. Check actual sources for a better insight. Very interesting technology and much smarter people working in this field who deserve a lot of praise.