What Are the Odds?

It’s my birthday, and Dave’s and Mary’s and Sean’s too! We’re in a neighborhood dinner group consisting of six couples. One evening a few years ago we came to the rather amazing discovery that of the twelve of us, four shared a March 18th birthday.

Now the chance that two people meeting on the street would share the same birthdate, say, March 18, is 1 in 365. The chance that three people would share the same birthday is 1 in 133,226. Add a fourth person and the odds are only 1 in 48 million they would share the same date of birth.

But the odds that those four don’t share just any date, but share March 18, drop to 1 in 17 trillion. Hey, it’s a special date!

If we assume the world population is about 7.3 billion, and we divide that entire world population randomly into little groups of four, there would be 1.83 billion such groups. If you did that grouping-by-four many different times and kept track each time how many of the 1.83 billion groups had all four members sharing the same birthdate (any date), you would expect an average of 38 such groups with each grouping.

The chance that among those 1.83 billion groups of four there existed one group of four that shared a March 18 birthday is 1 in ten thousand. That is, you would expect to have to regroup the world’s entire population 27 times to get one group of four that shared a March 18 birthdate. And the four of us live within a couple blocks of each other and get together every other month to share a meal with our wives and husbands.

The world sometimes turns out to be stranger and smaller than you imagined.

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