Now suppose that the adult population of the uni-activity world is 5 billion. To find the actual occurrence of the events in which we are interested, we multiply the probability by the number of times the experiment is performed. If the working day is 8 hours, each person performs the experiment 1600 times per day or, for a 5-day week, 8000 times per week. Let’s run the experiment for one year (52 weeks). Then each person performs the experiment 416000 times. And the entire world performs the experiment 416000 time 5 billion or 2080 trillion times. So the number of successes is 2080 trillion times the probability, or about 3785. Since there are about 260 working days per year, the number of jackpots is more than 14 per day! It is very likely that one worker hits the jackpot on his birthday, and the principle of “acausal coincidence” is not needed!
The real world is of course more complicated involving hundreds of activities rather than one. But the underlying idea of probability and the possibility of the occurrence of extremely rare events is the same. In fact, the law of large numbers in probability theory very generally states that when the size of a sample grows, so does the number of occurrences of a random outcome. Therefore, even extremely rare events (very small probabilities, smaller than the coin experiment above) in the real world do occur, because with thousands of years behind us, we have had a much larger sample in which to observe them.