Are there random events? Neither an affirmation nor a denial can redeem a confusion. Chance, or a random event, refers to the internal structure, or source, of an event if, and only if, that structure or source has not been allocated or identified. The idea of randomness as a "inherent property" identifies not the lack of a property, but a failure to denote the idea of one.
For example, the random movement of molecules in a gas or liquid, commonly called "Brownian motion" is random because we have not allocated structures to the micro-domains of groups of molecules; while the randomness of the outcome of a tossed coin is more a function of our failure to include a description of external influences, and of our arbitrary assignments of what counts as "face up" and "face down".
All of which begs the question, Are there events with no internal structure or identifiable source? The question entertains a mistake. The physical limits that constitute physical objects, events, and structures are set up by us through (epistemological) conditions; there are no inherent, standing forms waiting to be discovered.
We might cite quantum events or secondary properties like colours and sounds as examples of events that seem to have an innately non-attributable structure or unidentifiable source - in one sense at least - they come and go without adequate, or any, spatio-temporal redress. This would seem to suggest that randomicity can indeed denote an inherent property. However, randomicity, as I have defined it, need not be limited to physical events.
So, the impossibility of allocation of structure to the structureless (secondary qualities) or unsourced (quantum events) might only appear as an impossibility when, in fact, it represents a failure to change our epistemological conditions from the spatio-temporal milieu in which our ideas of randomicity are couched. For a quantum event the epistemological condition of "randomness" would refer to the mathematical and experimental domains of possibility in which the quantum event is set up.
The structure or source of quantum events, and by similar argumentation, secondary properties, can only be configured as inherently "random" if they are defined in a domain that is alien to their nature. This is naturally, though erroneously, permitted because the event itself, as against its structure or source, is reduced to (for it is a "reductionism") the world of the spatio-temporal.