RANDOMNESS must be defined as the inability to predict the outcome of an event..which you will see fairly at various sources of word definitions. Though such definitions does not make any claims suggesting randomness being the inherent part of the universe. Moreover, you might be assuming that if a reliable pattern is not found as well as reliable prediction cannot be surmised then there is a play of randomness, somewhere. Yet, just because a pattern has not been found or the predictions seems impossible to be sought out, doesn't mean there is no pattern. So, there lies the possibility of DETERMINISM, and thus all events/processes labeled as random are just 'apparently' random.
Obviously, the universe has a bunch of rules to be followed by its dwellers. That is, there are couple of aspects for any event to be truly random, what can be given as: Unpredictability and Randomness. Asking for something to be truly random usually means asking for more than it be just unpredictable. This is the point over which the seekers of Quanta battles the disciples of Sir. This is the battle for survival of the appropriate scientific belief that will guide us to the future where the notion of THE TRUE RANDOMNESS IS JUST THE MATTER OF PAST HUMAN MISBELIEFS. Yet, the battle still remains unconcluded, as the new opponent that is Quantum Mechanics comes into picture to defeat Newtonian Mechanics.
Let's take one-to-one examples from above two disciplines as to figure out the long sought answer..
The Butterfly Effect is the well known concept depicted in the eponymous movie - "The Butterfly Effect". which was nominalized from the famous plot of Lorenz attractor (as shown below).
The behavior of Lorenz attractor strictly depends upon the initial conditions and certain parametric values. Even the slightest change in the initial conditions shall result in large unforeseen result that sometimes can be predicted if accurate information regarding of the initial conditions is known, which in real world is greatly challenging to procure from natural-dynamic-processes. Thus, what seems to be chaotic in nature is not unpredictable at all, but pseudo-chaotic. I would suggest these processes are though non-linear and seemingly chaotic but they are driven by laws of Physics. Hence, this represents the deterministic behavior suggesting that nature is not so randomized at all. But, the information is greatly challenging for us to accurately observe at any moment that the process becomes seemingly unpredictable, and so random. Although the hope should be pertained that in distant future mankind will be able to collect accurate information about the nature that no processes or events shall be considered random or chaotic or unpredictable.
Let's take another example to suggest the deterministic behavior of nature that even tiny Electrons do follow. This is about The Single Electron Double Slit Experiment.
Inhere, electrons are sent into double-slit apparatus one at a time, resulting single point appearing on the screen, as expected. However, an interference pattern emerges when successive hits are passed through the slits. That is strange for an individual particle in a way that also shows probabilistic wave behavior.
Remarkably, what initially seems to be the random positioning of deflected electrons on the screen is guided by certain hidden parameters carried over along the particles, after they were originated from the gun. These hidden variables accounts for the precise location of each particle such that it forms an Interference pattern as shown in the adjoining figure.
Thus, it can be suggested that even the sub-atomic particles, in the quantum world, follows certain rules, although indiscernible but true, that is the reason they are called hidden.
The behavior of particles in quantum world can be even more spookier than what was been observed from the above experiment. As, in the quantum world there are no Newtonian Laws to lock particles with each other but this is a whole new alien world, whose mysteries are been unraveled by the quantum physicists.
So, in the end..who is the winner of this battle for truth. Well..I would suggests everything is the universe (or whatever you call it), seems to follow certain rules. Either understood or not, these rules determine the way everybody dances in the cosmic ball.