Sunday, June 2, 2013

Metor Crater Arizona : reseting my assessment of the probability of the improbable

I spent the last 2 weeks on a customer site in Phoenix, Arizona and had a free weekend. Saturday did a rim to river to rim in a day in the Grand Canyon (see ambitionexceedsability blog) and on Sunday went to Metor Crator in northern Arizona. I was the 1st in through the gates on the sunday morning, had quick look at the crater, took some pictures and was sitting in the film theater waiting for the film about how the earth might get destroyed by a metor impact, happy stuff. I was in a little world of my own thinking about the technical issues that I had been working on at the customer site about 150 miles south.

2 chaps walk into a film theater with a capacity of about 200 people and pick the seats right in front of me. One who looks very much like someone I know called Jon who is with someone who looks very much like Ed I know, looks at me, does a double take and then says "sorry, you look just like someone we know".

So lets do a rough guess at the probability of meeting this pair in the middle of the desert. I had no idea they were even in the US
The components I can think of are

  • Chances of Clive being in Arizona during a weekend : 1 in 500 (take the last 5 years as a guide, I have only been to Arizona once)
  • Chances of Jon and Ed being in Arizona at a weekend as part of a road trip from San Fransicso : assume the same
  • Chances of being there at the same time over a weekend : 1 in 100 (16 hours open over weekend = 256 hours, but should be skewed higher as we are likly to visit at start or end of day)
  • Chance of sitting in front of me in the theater (it was big enough to miss each other): 1 in 4
  • Chances of Clive visiting Metor Crater during a weekend in Arizona : 1 in 4 (I only decide to visit it about 1 hours before I meet them, I saw it on the map and thought that looks interesting. I could very easily have gone the other direction to see something else. My original plan was to go into the Grand Canyon on both days of the weekend.
  • Chance of Jon and Ed visiting Metor Creater during a weekend in south west US : guess at the same 1 in 4.
so that give a simple probability of around 1 in 1,600,000,000. I suspect  some curious bayesian influence are at play where the probability of meeting is in reality much higher.

We can assume a higher liklyhood as Jon and Clive share a subset of interests in things astronomy, so are likely to visit the same sort of areas. I guess I might know 100 or so people as well as I know Ed and Jon, so maybe the probably should be meeting someone I know well (whatever that is defined as).

Either way it would be a struggle to fudge the simple probability down to less than 1 : 1,000,000.

If anyone would like to comment with a pointer on how to calculate a more realistic probability, please do.

This does show that the probably of being found out is you are doing things you are not meant to is far higher than you think !

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