## Meteors and Money Management

I probably heard of Wethersfield, Connecticut, although I forgot about it until teaching a statistics course last academic year. The town vanished from my memory shortly thereafter, because as far as I know I’ve never been there or known anyone who had. The rather exciting meteor strike in Russia last week brought it back to mind, though, because the town worked its way into a probability book I was using for reference.

Here’s the setup: the town is about 14 square miles in area, out of something like 200,000,000 square miles of land and water on the surface of the Earth. Something like three meteors of appreciable size strike the surface of the Earth, somewhere, three times a day. Suppose that every spot on the planet is equally likely to get a meteor strike. So, what’s the probability that Wethersfield should get struck in any one year?

With that worked out the follow-up question, which becomes the obvious follow-up question when you learn why I think I probably heard of Wethersfield before the statistics course I taught, is what the chance is Wethersfield should be struck by two meteorites within an eleven-year stretch. There are at least two sensible ways to do that calculation.

What makes this a question worthy of getting into a statistics textbook is that Wethersfield was after all struck by meteorites, first on April 4, 1971, and second on November 8, 1982. The first strike was a touch before my time, and not really noteworthy enough to draw attention outside Connecticut, although the second launched the town into that fascinating realm of places designed for Ripley’s Believe It Or Not and probability word problems, and I’d have been the right age to be captivated by the evening news reporting on the event.

I have found mention of Wethersfield outside the world of probability problems by investment agencies, who want to point out that it may be ridiculously improbable that something might happen, but that doesn’t mean that it won’t. I am not personally convinced that meteorites in New England offer any financial planning advice, but I’m hardly in a position to say someone else is managing his money poorly.

Curiously, the two meteorites apparently struck locations about a mile apart, which should make the event even more remarkably improbable. But perhaps stating that two meteors strike a mile apart, eleven years apart, isn’t quite as naming a town to be hit.

## Geoffrey Brent (@GeoffreyBrent) 3:46 am

onWednesday, 20 February, 2013 Permalink |Working the numbers, rounding a lot, and skipping some second-order issues: Wethersfield is about 1/14,000,000 of the Earth’s surface, and 3 meteors/day = 12,000 over an 11-year period. For any given Wethersfield-sized area, the chance of getting hit by just one of those meteors is 12000/14000000, i.e. about 1/1000.

Of those 12,000 meteors there are about (12,000^2)/2 pairs, and for each pair there’s a (1/14,000,000^2) chance that BOTH will hit Wethersfield. So the chance Wethersfield will get hit by two meteors in a given 11-year period is about (12,000/14,000,000)^2 which works out at a bit under one in a million.

BUT if you divided the surface of the Earth up into Wethersfield-sized areas, you’d have fourteen million of them. Or about four million if you exclude the oceans. That means that you can expect about four such areas to experience a double-hit in that particular 11-year period.

A complication here is that we’re defining the intervals of interest (spacial and temporal) AFTER observing where the meteors hit, which means we may have cherry-picked those choices in a way that’s more likely to produce “coincidences”.

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## Joseph Nebus 4:44 am

onWednesday, 20 February, 2013 Permalink |I agree with you down the line, there, depending on just how you want to work out “just a bit under” one in a million.

The book I got it from — and I am trying to figure out where in my notes I wrote the source down, although I plundered the problem for homework — placed this in binomial distributions, where the young students returning to college after not thinking about algebra for years can try to imagine how you would even calculate “”, and then gives it a cameo appearance for Poisson distributions, which can be at least as terrifying to the calculator.

And, certainly, naming Wethersfield after the meteor hit makes it look like a longer shot than it should be. Saying that there should be about four Wethersfield-sized areas struck by two meteors every decade … well, that doesn’t quite make the idea any more accessible, since I still haven’t seen the town, and only occasionally appreciate just how big the Earth really is, but it feels more evocative.

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