If you are in a room with 22 other people there is a slightly greater than 50% chance that at least 2 of you will share the same birthday.
Do you doubt that?
It would be natural if you did. It’s counter-intuitive.
However, stay with me a little as I explain it.
If you are on your own in a room, the chances of you having a birthday unique to yourself is 100% – or 365/365.
If a 2nd person enters the room, the chances of them having a birthday unique to themselves is a little less than 100% – or 364/365 – because one day is taken by you. You can see that 364/365 is actually (365-1)/365.
If a 3rd person enters the room, the chances of them having a birthday unique to themselves is a little less again – this time it’s 363/365 – or (365-2)/365.
Etc…
When the 23rd person enters the room, the chances of them having a birthday unique to themselves is (365-22)/365.
Now the probability of all 23 having a birthday unique to themselves is calculated by multiplying all the individual probabilities.
That number comes out at 0.491 – or just less than 50%.
So if you flip that around, the chances of at least 2 people sharing a birthday is 1 – 0.491 or 0.509 – just over 50%.
So you only need 23 people to have a greater than 50% chance of 2 of them sharing a birthday. Maybe your classes at school reflected this?
The World Cup squads do! They’re 23 in size and 16 of the 32 squads have at least one shared birthday.
What has this got to do with your business?
Gut feelings can sometimes reveal the direction you should take – indeed sometimes gut feelings are all you have.
But not always.
Sometimes you have numbers to look at. And when you do, you should heed what those numbers are saying – even if the results seem counter-intuitive.
And, if you’re not mathematically inclined, and you’re wondering who can help you with data, the good news is that you know someone who is – you’re reading his blog post!
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