Thank you for your reply!
We'll never know a system that well that we can say it is random - as we will never know that a line in the real world is a straight line.
Both are mathematical structures. In Max Tegmark’s Level IV universe model, mathematical structures actually exist outside of space and time. What an observer "in" space/time would consider to be “real” is an illusion of that reality. Tegmark’s is the only closed physical cosmology known to me. All of the others get twisted pretzel-like in an attempt to explain the beginning (and end) of space/time and therefore, physical causality itself.
And we don't have to know this: we apply mathematics to our realities as long as this application works, i.e., leads us to predictions. And out of convenience, we'll say that radioactive decay happens randomly - and a beam of light is a straight line.
In General Relativity, a beam of light follows the curvature of space/time. And both radioactive decay and quantum fluctuations (classic examples of “random” phenomena in nature) are physically caused. They cannot be isolated as a self-contained theoretical “system.” Radioactive decay is an event caused by a collapse of the interplay between the strong nuclear force, electrostatic force, and weak nuclear force (perhaps also involving the gravitational force). It requires an activation energy to initiate (i.e., cause) the collapse. Quantum fluctuations are more interesting, because they are virtual particles which come into and out of existence in a vacuum. Nevertheless, neither event can occur in the absence of space/time.
One form of causality can be stated: But not for A, C would not be. If A is removed, C cannot/does not exist. In the absence of time, events cannot occur. In the absence of space, things cannot exist.
Thus I find Tegmark’s Level IV universe a superior physical cosmology.
What do you mean by "this universe is equally probable to any other universe"?
The atheist counter-argument to the theist observation that this universe is finely tuned for life is based on multi-verse physical cosmologies which conclude that all possible universes came into existence (plentitude argument, anything that can happen, did.) Their claim is that our universe is but one of all possible universes, equally probable to exist because all have existed - and therefore, that it happens to be finely tuned for life is moot. As one of them explained in a metaphor, for a customer to walk into a store where all possible sizes of jeans are stocked and find the one that fits him precisely is no big deal.
Their appeal to the plentitude argument (the fully stocked store) is a statement of faith - it cannot be supported by observation.