People need to keep in mind that randomness is absolutely embedded in the fabric of the universe through quantum mechanics - and that's been experimentally proven. You are correct. But is it random at the macro level as well?
I believe it is. And this gets to an idea I find fascinating. Is the universe determinate or indeterminate? If it's indeterminate how do non random processes evolve from a indeterminate universe? This has profound philosophical/theological as well as scientific implications. IMO.
.."God does not play dice with the universe"
Random doesn't mean unpredictable in the large. The outcome of casino games are completely non-deterministic (at least, the casino owners want them to be), yet the casinos can tell you how many winners and losers there will be. Randomness has it's own set of laws.