How Many Gregarious Mongolians Are There?

When I visited Mongolia 15 years ago, a young man approached us on the streets of Ulan Bator and offered to show us around. His name was Soyoloo, and we spent a few fun days hanging out with him.

I have many fond memories of Mongolia, so this NYT piece on Ulan Bator’s underground homeless population immediately caught my attention. The first picture is of a man named Soyoloo.  I wondered if this was the same Soyoloo I met so long ago.

How likely is that?  A naive estimate looks like this:  half of the one million people in Ulan Bator are men, so there’s a 1 in 500,000 chance that a randomly-selected (that is, randomly photographed) man from Ulan Bator is the man I met 15 years ago.  At 0.0002%, this does not seem very likely.

But here’s where conditional probability comes in.  The man in the photograph isn’t just any randomly-selected man; he’s a randomly-selected man named Soyoloo.  What I really want to know is, given the condition that a randomly selected man from Ulan Bator is named Soyoloo, what is the probability that he’s the man I met 15 years ago?

Naturally the answer depends on how many men in Ulan Bator are named Soyoloo.  “Soyoloo” doesn’t appear on any list of most popular Mongolian names, so I am going to estimate that at most 0.5% of Mongolian men are named Soyoloo (this would be roughly equivalent to ‘Andrew’ in the US, the 35th most popular male name).  This means that at most 2,500 men (0.5% of 500,000) in Ulan Bator are named Soyoloo.  Therefore, if a man in Ulan Bator named Soyoloo is selected at random, there is a 1 in 2,500 chance (0.04%) it’s the man I met.

This is the power of conditional probability.  The man in the photograph and the man I met share a common characteristic:  being named Soyoloo.  Knowing this condition greatly alters the probability that they are the same person.

In fact there’s another characteristic the two men share:  they are both comfortable striking up relationships with foreign strangers, whether it’s me or a photojournalist.  Let’s call this characteristic gregariousness.  Now the question is, what is the probability that a randomly-selected gregarious male resident of Ulan Bator named Soyoloo is the person I met 15 years ago?

Well, how many gregarious Mongolians are there?  Let’s say 5% of all Mongolians are gregarious.  Then there are roughly 125 gregarious Mongolian men named Soyoloo in Ulan Bator, and thus, a 1 in 125 (0.8%) chance that the man in the photo is the same man I met.  Not a lock, but not a longshot, either!

This probability may seem surprisingly high, given the distance in both time and space,  but I have a feeling it’s him.  His eyes look warmly familiar.