What are the odds?

This sounds like one of those interview questions: "How many petrol pumps are there in North America" sort of thing.

Perhaps you could start at the odds being one in six billion (number of people on the planet), and cut it down from there? Maybe that route will take a (lot) longer time...

ok, serious answer:

I would look at it like this:

1) On any given day, what % of folks in London are from LA?
2) How many folks use London Bridge (LB) tube per day?

From this, you get the number of LA peeps who use LB per day:
Flights per day LAX-LHR: 10
Seats per plane: 350
Avg occupancy of plane: 70%
Daily new arrivals from LA: 2,450
Avg stay in London: 14 days
# LA-ers in London per day: 34,300
London population: 7.6m
% London pop who are from LA: 0.45%

LB passengers per day: 187,500 (extrapolated from 07 & 08 LB exit data)

So assuming a tourist from LA is as likely as a Londoner to use LB station, you should have 851 LA-ers using London bridge per day.

The next step is to ask what is the probability that Aram's friend is one of those 851, and what is the probability that Aram is one of those 186,649? Moreover, what is the probability of them being there at the same time?

Might pick this up later, bit busy now. Someone else can run with it if they want to.

You also need to factor in frequency of tube services and looking at the LA peeps, you need to consider the percentage LAX-LHR passengers who are from LA and coming into the capital. Bear in mind the regression of passengers who are simply using that flight for convenience but then travelling on to other parts of the country or not leaving the airport at all be transfering onto other extranational flights.

Consider then the percentage of tube passengers who actually use LB and cross that against LAers in London altered for tourist density and tourist transport modes. You'd be lucky if the number of LAers exiting LB exceedes more than 100 identifiable individuals a day.

The really awkward factors that will be hard to determine will those of two people with a clear and direct connection who are within line of sight of each other actually noticing each other.

You also need to factor in frequency of tube services and looking at the LA peeps, you need to consider the percentage LAX-LHR passengers who are from LA and coming into the capital. Bear in mind the regression of passengers who are simply using that flight for convenience but then travelling on to other parts of the country or not leaving the airport at all be transfering onto other extranational flights.

True, not everyone arriving on such a flight will be an LA resident heading to central London, but then not every LA resident in central London will have arrived on such a flight. In the absence of any hard data, I'd just assume the two cancel each other out.

Consider then the percentage of tube passengers who actually use LB and cross that against LAers in London altered for tourist density and tourist transport modes. You'd be lucky if the number of LAers exiting LB exceedes more than 100 identifiable individuals a day.

187k is the number of passengers passing through LB tube station per day. The key assumption I made was that a tourist was as likely to use that station as a Londoner. Maybe it's more weighted to Londoners, since it's a big commuter station, but on the other hand, it's a pretty key hub for tourists getting around London. Again, in the absence of hard data, I'd assume that a tourist was as likely to be there as a Londoner. Same argument goes for 'tourist transport modes'.

The really awkward factors that will be hard to determine will those of two people with a clear and direct connection who are within line of sight of each other actually noticing each other.

True. But that Aram's a pretty observant fella :)