I'm going to link to an observation that I find interesting and then make a hard conceptual turn. Hang on.
Why don't our minds intuitively grasp probabilities? Scientific American suggests one appealing reason for not noticing the bigger picture: thinking statistically would require us to have perception attuned to movement on the grandest and smallest of scales:
Folk numeracy is our natural tendency to misperceive and miscalculate probabilities, to think anecdotally instead of statistically, and to focus on and remember short-term trends and small-number runs. We notice a short stretch of cool days and ignore the long-term global-warming trend. We note with consternation the recent downturn in the housing and stock markets, forgetting the half-century upward-pointing trend line. Sawtooth data trend lines, in fact, are exemplary of folk numeracy: our senses are geared to focus on each tooth’s up or down angle, whereas the overall direction of the blade is nearly invisible to us....
We are not equipped to perceive atoms and germs, on one end of the scale, or galaxies and expanding universes, on the other end. In the Middle Land of speed, we can detect objects moving at a walking or running pace, but the glacially slow movement of continents (and glaciers) and the mind-bogglingly fast speed of light are imperceptible.
I have a couple of thoughts on why this is so.
One, experience, tied to a quantum state, is ineluctable. And quantum theory tells us that all histories are possible. This history, the one you and I live on a macro scale, has emerged from those possibilities. We don't intuitively grasp probability because we can't grasp everything.
While we demonstrably can't understand the full sweep of events described by probability, and while we too often use story to puzzle over a family tragedy, or to explain (or explain away) the Black Swans that materialize from nowhere, experience need not be simply experienced.
Strangely, one result of tragedy might be tenderness, which, having been conceived in our brains, might find its way via our nervous systems and empty into the extended arms of a warm embrace. Despite every injustice, we can also choose to forget, choose to miscalculate, choose to misperceive. In such cases our folk numeracy serves us well. Damn the probabilities.