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]
[1] http://en.wikipedia.org/wiki/Local_hidden_variable_theory