6.7.10

Week four in Kampala and I am loving it. Work is picking up and the people we've met are wonderful. There's the great members of the church, the NGO directors we've contacted, our favorite taxi driver, Alfred, and, of course, Dave and Jim, my fellow economists that work in a little grocery store down the street. We're always raving about Lionel Messi and Barcelona and counting down the seconds until the World Cup (there are about 260,000 left, by the way). We even let my dear friend and co-worker, Lauren Soelberg, enter our realm today, even though she's a Political Science major (I know, I think I'm going soft). Anyway, they are great guys and I love hanging out with them.

So, we take a lot of public transit in Kampala, mostly the mini-buses which are called Matatus (see below) and, as I was riding in one the other day, I thought to myself..."I wonder what the chances are of me riding in this same Matatu again before I leave Kampala." Well, it turns out that my chances are actually pretty good. But first I had to make a couple of assumptions (and buy myself a Coke).

Now, journey with me my friends: let's assume that there are about 500 Matatus operating in Kampala on a given day. Let's also assume that we take about 9 rides a week (which is pretty conservative) and that, in the next two months, no new Matatus enter or leave the assumed set. Now, using the following equation (derived from the birthday paradox), I can figure out my probabilities:

500!/ [500^n * (500 - n)!]

And here they are:
- After only one week, the probability of me riding in the same Matatu is only about 7% (0.0699).
- After two weeks: 27% (0.2663).
- After one month: 72% (0.725).
- After two months: 99.5% (0.9954).

Which is pretty cool. However, given the nature of the equation, I couldn't just stop there (I mean, who would?). Next I wanted to figure out how many Matatu rides I would have to take before the driver and I shared the same birthday.
So, assuming that it's the same set of guys that drive the Matatus everyday (and also maintaining our original identifying assumptions), these are the probabilities given the number of rides:
- For my first Matatu ride, the probability is only about 0.3% (0.00274).
- After the ninth ride (one week): 9% (0.0946).
- After the eighteenth ride (two weeks): 35% (0.3469).
- After the thirty-sixth ride (one month): 83% (0.8322).
- After the fifty-fourth ride (six weeks): 98% (0.9839).
- And, after the seventy-second ride (two months): 99.9% (0.9995).

Which is pretty sweet. Therefore, during my stay in Kampala, I am extremely likely to take the same Matatu twice and also to have the same birthday as one of my Matatu drivers. I was thinking that it might be fun to ask each of the drivers their birthdays over the next couple of weeks, but then I thought that might be going a little too far...*sigh*

Bon voyage!