Probability and uncertainty are so difficult for us to understand. A related, and equally important problem is how easy it is to underestimate rare events in a world as large as ours. With a large enough sample, any outrageous thing is apt to happen, states mathematician Frederick Mosteller.

There are about eight billion people on this planet. So, if an event has a one-in-a-million chance of occurring every day, it should happen to eight thousand people a day, or 2.9 million times a year, and possibly a quarter of a billion times during your lifetime. Even a one-in-a-billion event will become the fate of hundreds of thousands of people during your lifetime.

Physicist Freeman Dyson once explained that what’s often attributed to the supernatural, or magic, or miracles, is actually just basic math.

In any person’s normal life, miracles should occur at the rate of roughly one per month: During the time that we are awake and actively engaged in living our lives, approximately eight to ten hours each day, we see and hear things happening at a rate of one per second. So, the total number of events that happen to us is now about 30,000 – 36,000 per day, or over a million per month.

If the chance of a “miracle” is one in a million, we should therefore experience one per month, on average.

What’s different now is the sheer size of the global economy, which increases the sample size of potentially crazy things happening. When eight billion people interact, the odds of a fraudster, a genius, a terrorist, an idiot, a savant, a jerk, or a visionary moving the needle in a significant way on any given day is nearly guaranteed. To date, there have been roughly 100 billion humans to ever live throughout time. With an average age of 30 years, individual humans have lived approximately 1.2 quadrillion days (or 1.2 million billion). Crazy occurrences that have a one-in-a-billion chance of happening, mathematical speaking, have occurred millions of times!