People get confused because it's easy to look at a quantum mechanics problem from the wrong angle and see nondeterminism. We're really well trained in intuitive mechanics ("an electron is like a tiny tennis ball, and tennis balls are always either here or there, right?") so at first glance quantum mechanics seems wacky and random: the electron might be here, or it might be there, with equal probability, and we can't tell which! Whereupon your head explodes. Seriously: The discoverers of quantum exploded in horror, and they started ranting about that crazy cat in the box, or "God playing dice". (Colorful but misleading metaphors. One reason that Bohr and Einstein's early confusion persists today is that they were just so darned eloquent.)
In fact, God does not play dice: God sees all the outcomes of the dice roll at the same time and doesn't understand why we think it's a game, and not a static work of art.
People also think that nondeterminism is somehow an important ingredient in whatever it is we mean by "free will". This doesn't make much sense to me. If you want it to not make sense to you as well, read Daniel Dennett's Freedom Evolves. You might want to budget more than a couple hours for that book, though.
Edit. Nevermind, I see what you mean.
From [http://www.fourmilab.ch/hotbits/how3.html]
"But hidden variables aren't the way our universe works—it really is random, right down to its gnarly, subatomic roots. In 1964, the physicist John Bell proved a theorem which showed hidden variable (little clock in the nucleus) theories inconsistent with the foundations of quantum mechanics. In 1982, Alain Aspect and his colleagues performed an experiment to test Bell's theoretical result and discovered, to nobody's surprise, that the predictions of quantum theory were correct: the randomness is inherent—not due to limitations in our ability to make measurements. So, given a Cæsium-137 nucleus, there is no way whatsoever to predict when it will decay. If we have a large number of them, we can be confident half will decay in 30.17 years; but if we have a single atom, pinned in a laser ion trap, all we can say is that is there's even odds it will decay sometime in the next 30.17 years, but as to precisely when we're fundamentally quantum clueless. The only way to know when a given Cæsium-137 nucleus decays is after the fact—by detecting the ejecta. A Cæsium-137 nucleus which has “beat the reaper” by surviving a century, during which time only one in a thousand of its litter-mates haven't taken the plunge and turned into Barium, has precisely the same chance of surviving another hundred years as a newly-minted Cæsium-137, fresh from the reactor core."
The short answer is that in the many-worlds interpretation, this too is a deterministic process. The total wavefunction of the whole system (atom + observer) evolves deterministically. What isn't deterministic is "your" subjective view of it, but "you" only view a vanishingly small slice of reality.
Sorry, that's the best three-sentence explanation I can come up with right now, and I admit it's only a shade better than "trust me, I'm a physicist". But trust me, I'm a physicist.
I'm game if you are, though. You might start by thinking about a modern digital computer. It's made up of a very large number of very small devices (transistors) that sling populations of electrons back and forth. The brain is made of a much larger number of less-small devices called neurons, that sling bigger populations of bigger objects (organic molecules) back and forth. So according to the basic understanding of QM that tells us relative indeterminacy increases when considering smaller objects, the functioning of the human brain is marginally more predictable than the insides of a modern computer.