I’m trying to work out a formula for calculating the probability of two or more people sharing the same First Name, Surname and full date of birth (Day/Month/Year), from a given population.

I know the population size and the number of people who have any given name within the population.

I tried reading through it all, but it is Friday I gave up on the original question and pondered on the odds that I’ll consume more pints than the number of emoji pints in this sentence.

'The assumption that people have first name & surname limits the problem somewhat. You’re well into ‘falsehoods programmers believe about names’ territory. You can say ‘In the UK’ to mostly (but not completely) solve that.

The second problem is that whereas surnames tend to be passed down in families and don’t change much, first names can be absolutely anything you can form into a word. And the distribution isn’t remotely equal, because the probability you will have someone called ‘Dave’ is far higher than ‘Flintlewoodlewix’, so it’s not a simple calculation.

I don’t have nearly the maths to make a sensible number out of it. The probabiliy that someone has the same name is probably relatively high once you filter outliers (say, take the top 10,000 names and ignore the others) - birthday paradox and all that.

Thinking about it a little more the probability depends what that name you’re talking about. Probably quite a few ‘Dave Smith’ out there… so there won’t be a single number you’re looking for.

Thanks. It’s to do with the likelyhood of false positives. Apparently David Smith is the most common name in the UK, so if we can use that as a worst case example, and use the UK population, is there any figure I can arrive at? If I say there are 10000 David Smiths and the UK population is 60 million?

That link @davidwalton posted I think suggests that you would need 579 people with the same name for there to be a 99% chance that two or more of them have the same DOB. I don’t really understand how they arrived at that number, it’s a bit technical for me!!