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Try to wade through this quotation from statistics professor Tom Leonard (University of Warwick)...and the subsequent note. They are worth it.

"A particular coincidental event has, by definition, an infinitesimally small probability of occurring. However, there are infinitely many events which might possibly occur coincidentally to a particular person but, as it happens, do not occur. If we summed over all possible coincidental events, then we could find the probability of at least one of them occurring during the person's lifetime to be quite sizeable. I would be surprised if many people could say that they have never experienced an extreme coincidence.

The best coincidence yarn I know of runs as follows. In his first lecture at this university, a new professor of statistics was describing the laws of probability to his students. To illustrate them, he removed a coin from his pocket and tossed it in the air. It landed on a polished floor, spun around a few times, and to a thunderous applause came to rest--vertically on its edge! The point is that this was one of many coincidences that might have happened."

Another mathematician, Warren Weaver, has calculated that the chances of a coin landing on its edge are approximately one billion to one.

Source: A. Vaughan, Incredible Coincidence: The Baffling World of Synchronicity, 1979, pp. 198-199.