According the Copenhagen Interpretation, the probabilistic nature of quantum mechanics predictions cannot be explained in terms of some other deterministic theory, and does not simply reflect our limited knowledge. Quantum mechanics provides probabilistic results because the physical universe is itself probabilistic rather than deterministic.
Put another way, a system stops being a superposition of states and becomes either one or the other when an observation takes place. Some interpret the Schrödinger's Cat experiment to mean that while the box is closed, the system simultaneously exists in a superposition of the states "decayed nucleus/dead cat" and "undecayed nucleus/living cat", and that only when the box is opened and an observation performed does the wave function collapse into one of the two states.
In essence, the cat is alive until you open the box. Once you open the box, it is this act of observation that kills the cat.