I have been reading an excellent book by David J. Hand, The Impossibility Principle: why coincidences, miracles, and rare events happen every day, (2014), that discusses the mathematical framework of concepts that we commonly hold to be “miraculous” or “extraordinary” events. The basic premise of the book is that happenings that we think of as coincidences, are actually inevitable. Part of the reason for the inevitability of such occurrences is the Law of Truly Large Numbers.
The Law of Truly Large Numbers states that, provided enough “opportunities” (i.e. chances for a given event to occur), any outrageous event is likely—if not guaranteed—to occur. For example, the odds of winning Powerball Lottery are roughly 1 in 175 million. These odds are enormous, as is, but consider what the odds of winning the lottery twice are—about one in one trillion.
Yet, think of all the people that play the lottery, and the number of tickets for a given Powerball lottery drawing that are sold for each time a drawing is held. Because a massive number of opportunities arise (here, the number of tickets sold, and their attenuate number combinations), and because there are a finite number of possible combinations of numbers that can be drawn (the 6 integers that are chosen on the night of the drawing), it is nearly inevitable that someone will win the lottery—and that someone, at some point, will win the lottery twice. (Note: Don’t confuse individual odds with collective odds—while the odds that you or I win the lottery twice are microscopic, the odds that someone will win the lottery twice are, as shown above, inevitable.)
And several people (including Evelyn Marie Adams, who won the NJ Powerball twice) have, in fact, won the lottery twice. At least one person, Mike McDermott, has won the Powerball lottery twice using the same numbers each time.
The point here is to begin to think of events that, at first blush, seem unlikely or impossible as inevitable, provided enough opportunities for the event to arise occur.