# What are the odds of this spooky coincidence?

The coincidences we observe and the ones we often don't...
08 September 2023

## Question

I was waiting for my flight from Durban to Johannesburg to take off. I shuffled my playlist and ELO's last train to London came on. The first lyric is, it was 9 29. I checked the time and it was 9 29. I have 493 songs in the playlist totaling 34 hours and 19 minutes. What are the odds of this happening?

James - Well, John, what a great question. We'll try not to let you down and I know just the person to help me. University of Cambridge statistician, David Spiegelhalter.

David - I mean, it's a beautiful story. I love it. I love it. We need to think of it, first of all, in terms of assuming the song is played - he's going to play that song at some time in the day. What's the chance of it matching in that way? Well, I mean, let's assume that he plugs into his earphones 16 hours a day. He could do, and that's about a thousand minutes, but it could be morning or evening. I'm going to allow that. So out of the thousand minutes in which this song could be played at that particular moment of the song, the first line, two of them, would have this match. So that's a one in 500 chance, which is low, but not ridiculously low. The nice thing is that he observed this and what that reveals is that actually for all the coincidences that occur and that we notice that are so lovely, there are vast numbers that occur and we don't notice.

James - We've kind of butchered his question somewhat because the reality is he's not listening to this song all the time, or he just happened to hit shuffle and this one came on. But to even begin to calculate the odds of that, we've got to consider things like how often John is listening to music and then crucially, I suppose, what songs he has in his playlist and how many of them even contain references to time?

David - Yeah. You've got 34 hours, let's say the song lasts three minutes or so. We don't know how often he goes through that playlist. And so to work out the unconditional probability of this event happening to him, we would need to have a lot more information. The other thing which you mentioned is, are there other songs that mentioned time? And what it reminds me of is a wonderful art exhibition called The Clock, which I saw at the Tate Modern in London a few years ago. And all it is is clips from film and television of segments that at some point will show the time: somebody will look at their watch, the camera will spot a clock on the wall, and that time is always the time at which the film is being shown. It's full of all sorts of really obscure bits of TV and film which just feature the right time.

James - Yeah. What an incredible project to have undertaken.

David - Oh, just the thought of sorting through vast amounts of old films is quite extraordinary.

James - Thanks to the University of Cambridge's David Spiegelhalter.