Randomness could be described as a case of "
Not enough information" or an insufficient
model
If you ask someone to describe a random process, chances are they will say "A coin toss" or "Throwing dice". In the case of the coin toss, it isn't too hard to imagine that if you knew enough about the coin and the speed and direction of the toss you would know the result of the toss every time. The same thing goes for the dice, but you would have to know a lot more: the physical characteristics of the dice and the surface they're thrown on for instance.
Some clever people might suggest nuclear decay instead of the more hands-on coins and dice. Well, I'm not entirely up to date on the current state of quantum mechanics but I think most physicists would agree to the fact that if we knew everything about the state of a radioactive isotope we would be able to say exactly when it would decay. The problem is: we can't really know and the models we have been using for some time are not good enough to describe this process in a deterministic way.
Isn't this great? No more surprises!
Sorry... there's still the problem with Not enough information...