(WS) Chance encounters

Summary

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More or Less (WS): Chance Encounters

BBC World Service | Host: Angela Saini (June 18, 2012)

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Episode Overview

This episode of "More or Less" dives into the mathematically fascinating world of coincidences. Angela Saini, standing in for regular host Tim Harford, unpicks stories about remarkable chance encounters and reveals, with the help of expert mathematicians and statisticians, how likely these “amazing” coincidences really are—or aren’t. From accidental encounters abroad to choir sign-ups, the episode unpacks the math and psychology of “What are the chances?”

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Key Discussion Points & Insights

1. The Allure and Perception of Coincidences

• Introduction to Theme: The episode is prompted by a listener, Ken, whose friends have encountered acquaintances in distant foreign locations—seemingly against all statistical odds.
• Angela Saini's Take (00:12 – 01:22): Even the host herself experienced such a “coincidence” in a New Delhi cafe, bumping into a London friend.
• Notable Story: More or Less once received a question from a listener in Malawi, only for a Malawian producer in London to recognize the name—revealing unexpected connections can crop up everywhere.

2. The Boss on Holiday Story: Calculating "Impossible" Odds

• Charlotte’s Anecdote (01:59): Her friend Catherine, having called in sick to her supermarket job to go on holiday, discovers her boss occupying the balcony above her in the same Spanish resort.
• Explaining the Math:
  • Mathematician Katie Chico (02:44 – 04:24):
    • Probability of Choosing the Same Week: Roughly 1 in 7.
    • Probability of Choosing Spain: About 1 in 3.
    • Combined Chance (Week + Spain): Around 1 in 20.
    • Further Narrowed—Magaluf Resort: Out of 800,000 UK travelers, 20,000 go to Magaluf (probability for Magaluf: ~0.025, or 2 in 100).
    • Final Odds (Week + Magaluf): Around 1 in 1,000 if choices are independent; but the reality is, they almost certainly used the same travel agent, reducing the “coincidence” considerably (“At any one time, a travel agent will have the same best deal on offer.” [05:00])
• Lesson (Katie Chico, 05:10):
  “If you want to avoid going on holiday with your boss, then don't use the same travel shop as them.”

3. The Psychology of Coincidences: The Law of Truly Large Numbers

• Statistician Byron Jones (05:35):
  • Key Insight: We personalize coincidences and search for deeper meaning, but in reality, the sheer scale of human interactions makes surprising encounters almost inevitable.
  • Quote:
    “Friends are bumping into each other globally all the time… that event in itself is not that unusual.” (05:39)
  • The Law of Truly Large Numbers Explained: Given enough opportunities, highly unlikely events actually become likely to happen somewhere, to someone.

4. Choir Coincidence: Three Members, One Street

• Julia’s Story (06:01): Three new members join a rock choir—turns out, all three come from the same distant town and the same street.
• Maths Dissected (Katie Chico, 06:50 – 08:05):
  • Catchment Area Estimate: 10-mile radius, about 5,600 streets.
  • Initial Probability (Random): 1 in 31 million for three unrelated people from the same street.
  • Adjusting for Reality: The choir advertised heavily in their hometown, and the kind of people likely to join narrows it further—to 116 “likely” roads.
  • Final Probability: 1 in 30,500—making it “about as likely as you'll be injured in the toilet this year.” (08:49)
  • Memorable Delivery: The odds are sung by the rock choir itself.

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Notable Quotes & Memorable Moments

• Angela Saini, introducing the concept:
  “What if I hadn't been available? Maybe it would have been more of a coincidence if we'd both been on holiday at the same time.” (00:22)

• Mathematician Katie Chico on travel agents and coincidence:
  “So the chances of this happening to Catherine are not that slim. … If you want to avoid going on holiday with your boss, then don't use the same travel shop as them.” (05:10)

• Statistician Byron Jones on perspective:
  “What we don't really appreciate is that friends are bumping into each other globally all the time, … and that event in itself is not that unusual.” (05:39)

• Choir’s sung probability statement:
  “Given all the data we've got and assumptions we have made, the chances of this … it's about 10,000 times more likely than a lotto.” (08:05, paraphrased)

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Timestamps by Segment

• 00:12 – 01:22: Introduction; personal and listener coincidence stories
• 01:59 – 05:16: The “Boss on holiday” story and Katie Chico’s step-by-step probability breakdown
• 05:35 – 06:01: Byron Jones discusses why we shouldn’t be surprised by coincidences
• 06:01 – 08:49: The “choir coincidence” story, with full analysis and probability “sung” by the choir

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Summary & Takeaway

This episode uses real-life anecdotes and expert analysis to show that remarkable coincidences, while emotionally powerful, are less improbable than they seem. By applying basic statistical logic and recognizing how probable-seeming odds are warped by large numbers and shared choices, the program highlights both the fun and the falsehoods of “miraculous” chance. Listeners are reminded: astonishing events are to be expected when you consider how interconnected—and how numerically massive—everyday life is.

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Transcript

[A]

Thank you for downloading from the BBC. For details of our complete range of podcasts and our terms of use, go to bbcworldserveys.com podcasts

[B]

this is more or Less this week we're looking at the statistically unlikely world of coincidences. Hello and welcome to More or Less the Numbers programme on the BBC World Service. Today, as you've no doubt noticed, we have zero Tim Harfords in the studio. I'm Angela Saini standing in for Tim while he takes a well deserved break. It just happens to be a coincidence that I was available. Or was it? What if I hadn't been available? Maybe it would have been more of a coincidence if we'd both been on holiday at the same time. Yes, you have guessed the theme of today's edition and our journey through the statistically unlikely world of coincidence begins by looking at chance encounters inspired by this question from listener Ken.

[C]

I know a number of people, including myself, who've bumped into people they know whilst a long way from both parties home. And with neither party having prior knowledge of their journeys, these stories are often accompanied with the question, what are the chances of that? The locations have included Florida, Australia, Vietnam and a fairly remote Mallorcan beach. So, more or less, what are the chances of that?

[B]

Ken, your friends aren't the only ones. In fact, the same thing happened to me once when I was in a cafe in New Delhi. I was ordering a drink when standing right next to me was a friend I knew from thousands of miles away in London. And then there was a time that more or less itself was struck with a case of synchronicity. A listener from Malawi called Sam emailed the program with a question. So we asked a Malawian producer who works with us here in London to read the letter out. He took one look at Sam's name and it turned out they'd been at university together.

[D]

Actually, I've got an amazing story that I reckon beats all these, though.

[B]

Charlotte, what's your story?

[D]

It happened to my friend Catherine. She wanted to go on holiday with her friends but she couldn't get the time off work, so she called in sick to the supermarket where she worked and went off on holiday. Anyway, anyway, when she gets there to the resort in Magaluf, she comes into her apartment, she goes out to take a look at the view and there she looks up and lo and behold, on the balcony above is her boss. What are the chances of that?

[B]

There's a morality tale in there somewhere, I think. So what exactly were the chances of her boss taking A holiday in the same apartment block. Well, this being more or less Charlotte, we should do that maths. So with some help, yes.

[D]

Katie Chico, a mathematician from the UK's Open University, has considered the case of My Naughty friend.

[E]

Well, if we start by knowing that Catherine's boss has booked a holiday in Spain, then we want to find out what's the chance that Catherine goes along and books holiday in the same place at the same time. If we assume that they're independent events, then the chance that Catherine books a holiday on the same week as her Boss is about 1 in 7, because they both want to choose a nice sunny summer holiday and they both want a cheap holiday. They don't have children, so they're going to avoid the school holidays. So we're looking at seven weeks in which they could book their holidays. On top of the chance of choosing the same time, we've got to look at choosing the same place. Brits generally are still choosing Spain as their most popular holiday destination. There's about a one third chance of Catherine choosing Spain as her holiday destination. So the chance that she both chooses the same week and Spain are 1 in 20.

[D]

But the statistical reasoning doesn't end there. It turns out there's a travel agent right by the place where Catherine and her boss worked. Now, our mathematician has taken the fact into account that it's quite likely they booked their holidays at the same place.

[E]

This Travel agent sends 800,000 people a year to Spain. And of the people they send to Spain, they send 20,000 to Magaluf, the resort where Catherine was caught red handed. So the relative probability that a person selects Magaluf as a destination, given that they've selected Spain, is 0.025. It's about 2 in 100. So the chance of Catherine selecting Magaluf, all other things being equal, are about

[F]

eight in a thousand.

[E]

And the chance that she selects the same week and Magaluf is about one in a thousand. Now that's if we'd assumed all along that the events of Catherine choosing Magaluf and her boss choosing Magaluf are independent events. But of course they're not going to be independent. They use the same travel agent, they use the same travel agent shop. At any one time, a travel agent will have the same best deal on offer. So if two people walk into the same travel agents within a similar period of time and ask for similar holiday requirements, it's very likely that they're going to be offered the same holiday. So the chances of this happening to Catherine are not that Slim. And the lesson here is, if you want to avoid going on holiday with your boss, then don't use the same travel shop as them.

[B]

So this amazing anecdote isn't quite as amazing as it first sounds, is it?

[D]

I still love it, though.

[B]

And what happened to your friend Catherine in the end? Was she fired?

[D]

No.

[B]

Well, that is amazing. But even then, there's something we seem to love about coincidence, isn't there? Some of us might call it fate. Statisticians would call it the law of truly large numbers. Here's Byron Jones, a statistician in Switzerland.

[G]

With regard to coincidences, I think we tend to personalize them. And when we meet a friend in some distant location unexpectedly, we tend to think that's very surprising. People look into it more deeply to try and see an explanation for it. And what we don't really appreciate is that friends are bumping into each other globally all the time, as it were, and that event in itself is not that unusual.

[B]

The law of truly large numbers, Byron says, tells us that we should expect to see unusual or surprising patterns, coincidences, just because of chance. It's like winning the lottery. It would be very surprising if it happened to you, but it's not at all surprising that it happens to someone. But of course, coincidences make such good stories. So here's a last one for you from a more or less listener called Julia. Julia belongs to a rock choir in a town in England. When three new members joined her group, nothing seemed odd. Until, that is, they got chatting. Not only did all three of these new members come from the same town 10 miles away, but they also lived on the same street. Before you get too excited, though, here's mathematician Katie Chico again. To pop your coincidence bubble around this

[F]

area, you've got a rock choir and rock choruses about 10 miles away from each other. So I took a 10 mile radius around this particular choir as being a reasonable catchment area for it. Now we know what its catchment area is. I needed to find out how many streets there are in that catchment area. We want to find out whether they're on the same street or not. Just how many streets could they have come from? About 5,600. If we then said these women were turning up independently from any of those streets, you'd be looking at a probability of about 1 in 31 million that you would get three of them living on the same street turning up randomly.

[B]

1 in 31 million. These odds make it sound like it is a remarkably unlikely coincidence. But Katie discovered that the choir, these members, had joined had been advertising in their hometown a lot. But what about them living in the same street again? By taking into account the kind of people who join choirs, Katie figured out there were 116 likely roads they could have lived in. So the final odds here's her answer, delivered by the choir itself.

[H]

Given all the data we've got and assumptions we have made, the chances of this Luke and Curry will sing for you today. It's about 10,000 times more likely than a lot. It's not betting on that I would like to take. It's about.

[B]

There you have it, a one in thirty and a half thousand chance. About the same odds. You'll be injured in the toilet this year thanks to Katie Chico and the members of Rock Chorus, which is led by Lauren Field. That's your lot for this week. As you've heard, it's no coincidence that your stories appear in the programme, so keep your feedback and suggestions coming in. The email is more or less BC Co for the website go to bbcworldservice.com more or less more or Less was presented by me, Angela Saini. The producer was Ruth Alexander and the editor, Richard Varden.

[A]

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