Tuesday, December 15, 2009

Chance Encounters - What are the odds of that?

Our world is filled with systems, patterns and biases. The laws of physics and the universe demand a certain amount of order in nature and our surroundings. Yet despite this we often encounter random or sometimes unexpected events. At a distant airport while traveling on business you bump into a colleague you haven’t seen in 10 years. On vacation while waiting in line to enter the Magic Kingdom on the 4th of July in Orlando you see an old acquaintance. These are coincidences that seem to be unlikely random events. Just how unlikely are these encounters.

One view of these encounters is to look at the probability on any given day that any two people in a population will meet assuming they are independent events.

Let’s take Disney for example. According to the 2008 Attraction Attendance report by TEA/ERA about 17,063,000 people visited the Magic Kingdom in Orlando for 2008. This means on the average day, the park sees about 47468 visitors. The probability of any given individual being in Orlando might be 47468 park visitors divided by the US population 304059000 which equals 0.000157. This is one chance in 6368. If everything was considered independent we would say that the probability of Bill and his old acquaintance being in Orlando at the same time would be:

P=0.000157*0.000157 which is 2.64E-8 ( This is a very small probability number).

The odds might be expressed as one chance in 40.5 million. Wow this seems extremely low, however, this is not how the problem is solved.

Assume Bill is a moderately connected networker that can keep track of 500 contacts between family, friends, work associates and old classmates. Now we have to know a little about Bayesian probability and look at the probability that given a person is already at the Magic Kingdom, what are the odds an acquaintance is there. For this we have to look at the probability that Joe or Greg or Marge or Megan are there. There is literally a pool of possible candidates that may be at the park the same day of your visit. We add the probabilities together.

P=0.000157+0.000157+….. for all 500 contacts. This now gives a probability of 0.078 or about 1 chance in 13 that one of the acquaintances are at Disney on the very same day. Factor in the 4th of July and 20% additional attendance and the probability changes to 1 chance in 10. Since most people enter in the morning through the same set of park gates, there is good likelihood that you may be there at the same time as an acquaintance.

Airports, Malls, Amusement parks are large hubs where people gather and often at specific times based on schedules or seasons. It is not all that uncommon to hear stories of two people meeting that have not seen each other in years. These types of events although random may not be as unlikely or coincidental as we think.


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