I understand sound and video processing and even machine learning applications, but in what way is encryption probabilistic (other than trying to guess passwords)?

I don't know too much about it, but I would assume that generating random values would be more efficient if it was built into hardware than if the software had to process it. So, instead of running through calculations to come up with multiple random values, it would be a streamlined because the processor would have it hard wired in.

Ahh, that I can see, but is the bottleneck in encryption really in generating the random numbers? I guess the part of encryption I was focusing on is the part that does heavy-duty bit-crunching during the actual encryption/decryption process, which must be exact if you want to get back the same data you started with.