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Jan182011

## The unlikelihood of improbable events

I picked a couple of old books off my shelf last night, to sit by the fire and read something on paper for a change. I chose two classics by Darrell Huff: How To Lie With Statistics (1975 edition), and How To Take A Chance (1965 edition). They are both excellent, and the former is even still in print. The amusing story shown here (right) faces the first page.

I was a bit surprised this morning when the first thing I see, via Twitter, is this story from Reuters: wounded fox shoots its would-be (and unnamed) killer in Belarus (of all places). I thought this was quite a coincidence.

What are the chances of this being a true story, and not some sort of mistake, or hoax, or piece of folklore? At first, I thought of Bayes' theorem:

$P(A|B) = \frac{P(B | A)\, P(A)}{P(B)}.$

With this equation, we can calculate the probability of the story being true, given the chances of such a thing happening in the first place (slim), and the reliability of the media (pretty high). If you think the chances of a man being shot by a fox are 1 in 1000, say, and the reliability of the media is 99%, then Bayes' theroem suggests that the probability of this story being true is just 9%.

Nine percent seemed pretty low to me. Maybe I was being too hard on the media, I thought.

But then another thing I just saw yesterday was that Google News now searches archives going back over 100 years. Amazing. So I searched for fox shoots hunter, and hit Archive. And sure enough, it turns out this sort of thing happens all the time.

Shown here (left), the Wilmington Morning Star, 21 January 1981: A fox shot and killed (!) an unnamed hunter in central Yugoslavia after hitting the animal with his rifle butt.

Another story, from the Modesto Bee of 16 November 1948, details another nasty fox-shoots-man-after-man-tries-to-wallop-injured-fox-with-rifle incident.

So, I don't know if this story is true or not, but personally I doubt it. Looking at how it has spread like rabies through the media though, I think it's fascinating how these tales become part of our experience. No-one knows where it started, and a bit of digging suggests it may even be doubtful.

How many stories like that are there in the organization where you work? And how will you question the next one you hear?

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You're not going to go all Black Swan on me, are you? Anyway, my life is all about probabilities and likelihoods right now, so thought I'd share this funny with you.

January 18, 2011 | Maitri

Matt,

I thoroughly enjoyed reading this post, having recently written on the same subject, albeit from a different angle, here: http://thedailymaul.com/?p=1115

David

January 18, 2011 | David Brensilver

@Maitri: Thanks for the link - funny. As usual with probability, I get the beginning, I get the end, but it all gets a bit fuzzy in the middle.

@David: Cheers... I thought your riff was brilliant. I love how these foxes all got a second chance. I mean, what self-respecting hunter would try to whack the fox over the head with his rifle butt? Yeah, I suspect 'poor journalism' is right.

January 18, 2011 | Matt Hall

Actually the fact point to a revolution in the Fox Community. Foxes have had enough and will nto take this any longer. They are now trained and fighting back. Those like Matt that wish to ingore this and find excuses will be sorry...

January 19, 2011 | @hollanders