Let's consider some sources of randomness in greater detail. Our demonstrative mnemonic for the influence such sources have will be hands emerging through the veil, as if to imagine a person so cloaked, with hands bared. In particular, we will be asking ourselves the following two questions:
Where does its veil lie? I.e. where is the boundary beyond which the source becomes unpredictable?
What is the reach of its hands? I.e. what is the extent to which the random source influences the world around it?
It may make sense to start off with the smallest such veils. The radioactive decay of an atom, though not literally the smallest, represents the sort of background stochastic influence that makes up the bread-and-butter of our quantum universe. Its veil lies at the level of the atom itself; outside observers can estimate the likelihood of its decay based off of the half-life of the atom, but cannot predict exactly when it will happen (and, if more than one path of decay exists, which path will be taken).
Its reach is generally miniscule; small enough that for most practical purposes it can be dismissed entirely. A single ejected particle is not likely to change the course of much at all, and it is only in great number that radioactive elements gain their notorious influence on the world. That said, context can change this situation. A single particle in a nuclear core may spawn a cascade of fission reactions. A single particle when entering a Geiger counter may change the perception of the safety / activity of the object being observed. A single particle may mutate just the right bit of DNA in a gamete to produce effects that may propagate for years to come.
But generally such quantum-level events are short-lived, their sheer number and miniscule size reducing their influence on the world to the utterly predictable through the Law of Large Numbers ⬈.
A coin is in the air, turning end-over-end. The tiny, subtle influences of how force was imparted onto it (i.e. chaos), and where, coupled with the tiny, subtle influences of the medium through which it rotates, lend the coin its randomness. A close enough eye (say, a high-speed camera attached to a super-fast computer) may be able to tell which way the coin will land, but to the human observers, the event is so fast and its influences so subtle that the outcome is unpredictable.
Moreover, its outcome will be used as the basis for a decision. Maybe it will be which team gets the kickoff [1]. Maybe it will be who has to take out the trash. Again we see the influence of context into the scope of its outcome. In theory the information contained in the result of the flip may propagate away from location of the flip at the speed of light, but in practice its speed and influence are limited and contained to the downstream effects of the decision being made.
[1]Because it is unpredictable, and because the coin favors neither party, coin-flips are often used to establish fair and equal treatment of two alternatives. In this case, the guarantees of fairness and equality rest on the fact that the stakeholders of its outcome lie outside its veil.
A person is asked to make a decision. If you know them well enough, their response may very well be predictable (maybe even obvious). However the less well you know them, and the more "evenly" balanced the decision they are being asked to make is, the more this person's response will appear to be random. The vast majority of a person's processing and thinking occur well beyond the veil of an outside observer, and so for this reason people can considered to be sources of random influence on the world.
IMPORTANT: Much of a person's response lies beyond their own veil too! With the power if intellect and introspection, each of us can examine our own inner state, reasoning about its structure, its causes and influences, and how we go about making decisions. Nevertheless, there always seems to be that "inner" veil, the point beyond which even our own processing appears as if it were a suprise to us. By the time any signal hits the waters of our conscious recognition, it has passed through influences unknown.
The reach of this random influence mirrors the reach of the coin-flip, writ large. In the current age, with so much individual empowerment and individual freedom, a person's influence (while nowhere approaching infinite) is large, and difficult to underestimate. A single determined person, moving confidently in one direction, has vast reach into the outcome of the world in which they find themselves embedded. We are powerful, you and I; our hands can work wonders. When these hands work together, the sky is the limit.