It all started with this….

### The Hypothesis

Yesterday I twice met someone I knew on the tube. Wondering if @jasonbelldata could calculate the chances of such an unlikely journey.

— Timothy (@TimTendo) April 22, 2016

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### My Immediate Response

@TimTendo What do you think this is, Challenge Anneka? Anyway….. leave it with me. pic.twitter.com/uAeWNYSgng

— Jason Bell (@jasonbelldata) April 22, 2016

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### The Short Answer

This is not the first time Tim has led me down a Liz Hurley shaped rabbit hole, let we forget the shoe size based on heel alone…. the internet does not forget Tim!

So, Tim, to answer your question. **Yes I could**…. the quality of the question determines the quality of the answer.

Job done, everyone celebrate with a drink, break out the bubbly, Cava all round! (I wonder if he’ll keep reading down…….)

### The Slightly Longer More Involved Answer

While the “yes I could” answer still stands, the quality of the answer is a different matter altogether. Mainly because the variables are completely wayward at this point. Take the population of London, 8.539m and the two friends Tim’s bumped into.

**(1 / 8,539,000) * 100 = 0.00001164%**

We really need a better set of variables to work this out in a more refined manner.

- How many people does Tim know?
- What time of day was the Tube journey?
- What’s the average capacity of a full London Underground train?

### How Many People Does Tim Know?

Psychologist Richard Wiseman says we know about 300 people by first name. Now Tim’s Twitter profile maintains he has 1,400+ followers but let’s be fair he could have bought some of those 😉 – so I’m sticking with 300.

### What’s The Average Capacity of a Full London Underground Train?

Different trains, well they have different carriages and capacities. So we’ll go with an average. There’s a nice list on Wikipedia. So I’ve got a Steve Reich (let’s see who gets *that* joke!) number of 816.

### What Time of Day Was Tim Travelling?

Passenger volume on the Underground is not a constant. You can have a percentage of capacity (or over capacity in the morning/evening rush hour), as the Economist has previously reported.

So depending on what line, the time of day and how many stops between departure and destination has a very large bearing on how many travellers Tim will encounter. Now as I don’t have that information to have our result is going to a fairly wide tolerance as not to be accurate.

### Let’s Try and Work Something Out

So assuming all of Tim’s 300 friends are on the underground at the same time in a busy station at a busy time of day. There’s no real nice way to work this out, looking around there are different theories but I’ll plump with this one.

**(Timmy’s Friends + People On The Train) / London Population**

**(300 + 816) / 8,539,000 = 0.01%**

Now that assumes a lot, the train is full and no one gets on or off between the stations. Even if over 10 stops 200 people get off and 200 new people get on, so 2816.

**(300 + 2816) / 8,539,000 = 0.03649%**

Still a small amount.

But that’s the end, because Tim bumped into *two* people he knows.

**(299 + 2816) / 8,538,999 = 0.03647%**

**0.03649 * 0.03647 = 0.001330%**

I’m still not 100% convinced that’s correct, for a varying number of reasons. The variables for a start are so inaccurate as we don’t really know them, we’re making guesses. You could safely add a 20% tolerant number line each side and still be way off the mark.

As Lee Schneider pointed out in his post on the same question:

*“First, it’s amazing that we can put a number to something that you might think of as random, like running into a friend. Second, the number delivered by our spectacular calculation was meaningless. No way everyone in New York is going to be outside at the same time and distributed randomly so I could run into them in a controlled way. Fuggaboutit! As the statistics professor put it, “These assumptions are ridiculous, of course!””*

But hey, Tim, we had a crack at it.