What A Coincidence!
Why do random draws so often have repeats?
20 November 2025
Each day on his BBC Radio 5Live show, presenter Matt Chorley picks out numbered balls from three bags to create a three-digit number between 1 and 650. He uses this to find a random constituency somewhere in Britain, and then asks listeners in that constituency to phone in with their personal connections with the area.
With 650 consituencies to choose from, you'd think it would be months before you might ever get a repeat, which would require a re-draw. But the astonishing fact is that after just 30 days of doing the draw, there will be a 50% chance that there will ALREADY have been one repeated number. By 50 days the chance of a repeat exceeds 80%, and by 100 days it's over 100%.
How can this be?
Matt Chorley's daily draw is very similar to the more famous so-called birthday paradox, in which it turns out that you only need to have 23 people in a room for there to be a 50-50 chance that two people in the room share a birthday.
The easiest way to prove these surprising outcomes is to work out what the chance would be of NOT having a repeat.
In Chorley's case, let's imagine that on day 1, he draws out constituency number 116 (Croydon East). The next day there are 649 other consituencies that could be drawn out, so the chance of him getting a different constituency on day 2 is 649/650. On day 3, there's a 648/650 chance that his number will differ from the previous two.
Continue this for 30 days, and the chance of getting no repeat is 1 x 649/650 x 648/650 x 647/650 x .....621/650. That works out to be 0.507, which is roughly 50%. And since the only alternative is that there HAS been a repeat, the chance of a repeat after 30 days is also about 50%.
But it doesn't FEEL like this should be the case, which is why listeners accuse the draw of being a fix, or a conspiracy, or claim that the balls just haven't been mixed up enough.
Randomness and probability can be very counterintuitive.
1 of 7 Older