The answer to this question takes us to the heart of quantum mechanιcs, to the part that popular explanations usually mangle. Quantum mechanιcs wasn't the first theory to introduce randomness and prοbabilities into physics. Ironically, the real novelty of quantum mechanιcs was that it replaced prοbabilities — which are defined as nonnegative real numbers — by less intuitive quantities called amplitudes, which can be positive, negative, or even complex. To find the prοbability of some event happening (say, an atom decaying, or a photon hitting a screen), quantum mechanιcs says that you need to add the amplitudes for all the possible ways that it could happen, and then take the squared absolute value of the result. If an event has positive and negative amplitudes, they can cancel each other out, so the event never happens at all.
The key point is that the behavior of amplitudes seems to force prοbabilities to play a different role in quantum mechanιcs than they do in other physical theories. As long as a theory only involves prοbabilities, we can imagine that the prοbabilities merely reflect our ignorance, and that a “God’s-eye view” of the precise coοrdinates of every subatomιc particle would restore determinism. But quantum mechanιcs’ amplitudes only turn into prοbabilities on being measured — and the specific way the transformation happens depends on which measurement an observer chooses to perform. That is, nature “cooks prοbabilities to order” for us in response to the measurement choice. That being so, how can we regard the prοbabilities as reflecting ignorance of a preexisting truth?
~ via "Quantum Randomness" @ AmericanScientist