(WS) Chance encounters
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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've guessed the theme of today's edition.
What question started the episode about coincidences?
And our journey through the statistically unlikely world of coincidence begins by looking at chance encounters, inspired by this question from listener Ken.
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, well, 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?
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 programme 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.
Actually, I've got an amazing story that I reckon beats all these, though. Charlotte, what's your story? 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?
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 the maths. So with some help...
Yes, Katie Shiko, a mathematician from the UK's Open University, has considered the case of my naughty friend.
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 a 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 one in seven 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 one third chance of Catherine choosing Spain as her holiday destination. So the chance that she both chooses the same week and Spain are one in 20.
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.
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.
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