As best anyone knows, quantum mechanical effects (like radioactive decay) really are purely and objectively random -- i.e., it is not the case that they appear random because of our ignorance of some deterministic processes. The not-actually-random scenario is called Local Hidden Variable Theory [1], and is ruled out by a series of remarkable experiments based on Bell's Theorem [2].
You can, if you are stubborn, create a theory of QM with non-local hidden variables, but it turns out to be just as weird as orthodox QM; but instead of accepting objective randomness, you have to accept faster-than-light interactions. One example is David Bohm's "pilot wave" theory. [3]
I guess that the "determinism" that I have in mind is physically called "superdeterminism" [1]. In this sense, the revolution of the universe has been predetermined at the moment of the Big Bang (or even before) and throughout the lifetime of the universe, the next moment in time has been and is completely determined by the previous moment in time.
You can, if you are stubborn, create a theory of QM with non-local hidden variables, but it turns out to be just as weird as orthodox QM; but instead of accepting objective randomness, you have to accept faster-than-light interactions. One example is David Bohm's "pilot wave" theory. [3]
[1] http://en.wikipedia.org/wiki/Local_hidden_variable_theory
[2] http://en.wikipedia.org/wiki/Bell%27s_theorem
[3] http://en.wikipedia.org/wiki/De_Broglie-Bohm_theory