I'm no mathematician, but my curiosity in this instance was peaked by a discussion I had with a friend who'd just returned from holiday in London.
To cut a long story short, they "bumped into" someone they knew on the tube (subway).
So that got me thinking, how on earth would you get started even attempting to calculate the probability of meeting someone on public transport in Central London ?
If you limit it to the "tube" as in this case, you have the following rough statistics :
- 10 lines
- Approx 270 stations
- Approx 4000 carriages across the fleet, average 6 carriages per train
- Trains running approx every 5–6 minutes 24x7x365
That's probably a tricky probability question as it is. But then what if we add in the rest of Central London transport ?
The "Overground" line that has :
- Approx 112 stations
- Approx 5 carriages per train
- Trains running approx every 5–6 minutes 24x7x365
Then you've got "Network Rail" (i.e. "heavy rail") which also covers a number of stations within the Central London geography :
- Approx 260 stations
- Approx average 6 carriages per train
- Trains running approx every 5–10 minutes 24x7x365
Finally, if you really want to put the cherry on top, I suppose you would also take into account buses (although due to traffic, in reality buses tend not to be as popular in London) :
- Approx 18,000 bus stops
- Buses arriving approx every 5–10 minutes 24x7x365