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Improbably Probable

It is relatively common to observe someone conflating the rareness of an event with the improbability of an event. Suppose you have three possible ways to spend your free time each day, and for simplicity’s sake, you have a 1/3 chance of choosing each. Further assume that your choices about what to do each day do not depend on what you did a previous day and that each day you face 3 different choices.

Question: at the end of two weeks (14 days) what is the probability that you would have picked any particular pattern of leisure activities? The answer would be (1/3)^14 or 2.1 x 10e-7. That’s right. You would have had a 0.000021% chance of having done that precise combination of activities (about 1 in 5 million). From this observation, you would not want to argue that, “well, there was only a 1 in 5 million chance that I actually did those activities for two weeks so I must not really have done them.” You see, ANY pattern of choices over that two week period would also have had a 1 in 5 million chance of having been selected, thus, the expected outcome would be for something improbable to happen.

I was thinking of this when I was listening to a football coach discuss how unlikely it is for a kid at age 6, playing youth football, to make it all the way to the NFL. What does this have to do with Broken Windows, cows or economics? We’ll just, perhaps, have to wait and see.

Happy Groundhog Day.

One Response to “Improbably Probable”

  1. Harry says:

    Happy Groundhog Day to Wintercow, who is in the barn.

    Ground Hog day is a big deal around here, especially with the members of the grundsow lotsch, where the entrance requirement number one is to speak Pennsylvania Dutch. I can imitate the accent, know a few expressions, but do not speak it.

    Punxatawney Phil did not see his shadow today. That means an early spring. He is as good as Michael Mann and the IPCC.

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