A Miracle Once a Month!

I have looked into the claim that a "miracle" (a one in a million chance) will come true for you once a month. I began searching for the stats that back this up. The first website I visited was a Sermon on the Thornhill Baptist Church which stated this:

"Our lives are practically sprinkled with them [miracles]. Someone has looked at the statistics of probability and has figured out that we can realistically expect a miracle to happen to us at least once a month. With all the different events that happen in our lives, the law of averages suggests that every 30 days or so we'll get one of those one in a million moments."

They called it the "law of averages." Further searching found the Scientific American article "Miracle on Probability Street" by Michael Shermer. But in this article Shermer attributes this to the "law of large numbers." So which is it? Or is it both?

The law of averages states is a lay term that actually "reflects bad statistics or wishful thinking rather than any mathematical principle". One example of the law of averages is the belief that a rare occurrence will happen given enough time. For example: "If I send my résumé to enough places, the law of averages says that someone will eventually hire me." According to wikipedia, "This may actually be true assuming nonzero probabilities and the law of averages is simply named in place of the Law of Large Numbers."

So the law of averages is the wrong term for this claim. Sorry Thornhill Baptist Church, your sermon was interesting and well-meaning but you used the wrong mathematical law. What you probably meant to say was, 'the law of large numbers suggests...' So lets take a look at this law.

(...to be continued)