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The Odds of Getting off the Elevator First

Last week, I got into an elevator in a 19-story residential building with a couple and two other people. I was going to the 13th floor (numbered 14 because of the prevailing triskaidekaphobic numbering system). Accustomed to waiting as lower-floor occupants exit first, I prepared myself for an extra minute or so to be added to my commute. Then something miraculous happened. My stop came first; everyone else was getting off above me.

What were the odds of making such a quick exit?

Let’s make some simplifying assumptions. There were three other sets of elevator riders (counting the couple as one set). Each set had about a one-third chance of getting off after me: There are six floors above mine, and 12 at my level or below (not counting the first floor, which doesn’t require an elevator ride). The chance of all three getting off above me was about one-third cubed, or one-in-27 — less than a 4 percent chance.

Let’s round the estimate to 5 percent to account for the possibility that some hardy people take stairs to the lower floors.

Five percent. OK, it wasn’t a miracle, but it seemed like a rare event. Let’s call it a near-miracle.

Carl Bialik was FiveThirtyEight’s lead writer for news.

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