Hi irelandscape, thanks for the comment.
I am trying to argue that scientists are using math to predict only the time-averaged probabilities of individual random events.
Each random event is the fundamental physical reality and not the time-averaged values. We don't yet have the math to predict when individual events will happen.
However, the weird part that I don't understand yet is just why do these random events, when time-averaged always come to the same values?
You nailed it!