It is more than that.
The mathematics of probability discovered by Pascal and Fermat are models of repeated events, a fiction. The model, their model, is founded on induction that fails to account for The Black Swan unique event.
Hardly. Measures of dispersion are an integral part of statistics. By the way, you're still confusing probability with statistics.
Probability involves using the knowledge of any system, whether that be as simple as flipping a coin, or as complication as a deck of cards and multiple players under the rules of Texas Hold 'Em, to predict the likelihood of future events. Inherent within the science of probability is the fact that predictions are not absolute. Thus, you certainly can flip a penny fifty times with it landing heads all fifty times. But the probability of that happening is cut in half each flip. This, it's 50% for the first flip, 25% for the second flip, 12.5% for the third, etc. The probability that it will land heads all fifty flips is 8.88x10[SUP]-14[/SUP]%. Science never says that it's "impossible." Science says that it's "highly improbable," and because it is indeed science, and not "a fiction" as you errantly claim, science also tells us the precise value of the probability.
Statistics, meanwhile, is the measure of historical information in a way that provides meaningful analysis.
As others, California Right To Carry et al, here have noted, our studies must go deeper than the fly covers of the books that we reference.
My studies include a Master of Science in Management, a principle component of which is the thorough understanding of both probability and statistics. That's two years of hard labor, er., study, and I went deep enough to earn a 4.0, graduating Summa Cum Laude. Prior to that I studied engineering statistics (full year), business statistics (another full year), graduate-level statistics (three classes, each with its own 1,000+ page textbook). Somewhere along the way I became a registered statistician. Alas, that was before Uncle Sam asked me to fly airplanes, so my accreditation has long since elapsed. Even so, I keep up the skills, as my profession requires it.
Is that "deep" enough for you?
Put more simply, I don't have to read your damned book when I have half a dozen texts of my own lining the bookshelf about a foot above my monitor.