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World Cup squads and the Birthday Paradox

World Cup squads and the Birthday Paradox
By Mark Mason on 16-05-18 10:28. Comments (0)
England's squad for the 2018 World Cup is being announced today. 23 players will make the trip to Russia - and coincidentally 23 is also the number at which the chance of two people sharing a birthday reaches 50 per cent. In fact it's a shade over: 50.73 per cent. Yes, you read that right - with just 23 people gathered together, it's more likely than not that two of them will have the same birthday.

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Big Ben

On a visit to Big Ben, I was told that if you stand at the bottom of the tower with a portable radio and listen to the chimes on Radio 4 (they still transmit them live), you hear them on the radio before you hear them ‘for real’. I couldn’t believe it – but was intrigued enough to try it for myself. And you know what? It’s absolutely true. The bongs come out of the radio a fraction of a second before they reach your ears from the top of the tower. It’s something so silly, so counter-intuitive, that you have to tell people. (Well, I did.) Researching the explanation, I found that it’s because radio waves travel at the speed of light (186,000 miles per second) rather than the 700 or so miles per hour at which sound waves travel. The signal travelling down the wire from the microphone to the BBC goes at the speed of light too. Hence the radio version overtaking the real one.

I realised that this would be the perfect way to teach the principle in school physics lessons. Instead of a boring teacher droning on that ‘radio waves travel at the speed of light’, illustrate it with this beautiful and quirky little fact. The kids will remember it then. I certainly would have done if my physics teacher had taken this approach. As it was I had to wait until I heard a piece of so-called ‘trivia’ in my thirties.