The probabilities in quantum mechanics don't mean there is no determinism. The "answer" to determinism is dependent on your interpretation of quantum mechanics. Even then, take the popular many worlds interpretation. Some see it as supporting determinism and some see it as not supporting it. I wish I could find the pbs spacetime video that talks about it much more eloquently than I can. Somewhat tangential but if you're interested take a look at the relational interpretation: https://en.wikipedia.org/wiki/Relational_quantum_mechanics . It doesn't get discussed much and it made me think differently about the topic.
Any interpretation that asserts a deterministic universe must invent a "hidden" mechanism which causes the apparent non-determinism, and which we cannot measure nor predict.
By Occam's razor, it is more probable that the universe is simply non-deterministic.
By themselves, they don't. But quantum probabilities are unique. They cannot be explained by missing information about local, pre-existing properties. Therefore, to maintain determinism, you are forced to accept extreme alternatives like non-locality (actions here instantly affecting the other side of the universe) or the existence of infinite splitting universes. If we reject those unobservable overheads, non-determinism is the most direct conclusion.
I'm not a fan of hidden variable theories. Every interpretation asks you to accept something weird. I like the relational interpretation because its weirdness is the least unpalatable to me (no hidden variables, no non-locality, no unobservable "other worlds"). To me the relational interpretation gives an explanation for how certain information can only be predicted with probabilities without requiring some fundamental randomness. The simplified example is that when you measure the spin of an electron the value of the spin only makes sense relative to the thing that measured it. It's essentially just extending to quantum mechanics the idea that the velocity of a thing means nothing without another thing its velocity is relative to.
