Wednesday, June 18, 2008

Severed feet and probability

A colleague mentioned this bizarre story today about a severed foot washing up on the shore of Vancouver Island. Over the past 11 months, a total of six human feet have been discovered on British Columbia shorelines. Besides the strange fact that only feet (and no other body parts) are washing ashore, is the statistically improbability that there have been five right feet and one left foot. It's been suggested that the feet are from the bodies of a plane crash three years ago.

The story got me thinking about the probability of 6 non-matching feet from 6 bodies. It's a bit like one of those programmer test logic/probability puzzles, only more morbid. How likely is it that six feet from six unique bodies would wash ashore?

Assuming there are six bodies, the sequence of probabilities for discovering unmatched feet is:

With six bodies and six unique feet, the probability is just less than 7%, which suggests that the feet more likely are from a pool of more than six bodies.

More generally, the probability works out to:

where a is the total number of bodies and b is the number of feet found so far.

If you want to play with the probabilities (perhaps as more feet are discovered), you can use the attached spreadsheet.