UKC

It's rather trivial to show that a random group of 23 has a better than even chance of having a birthday coincidence.

I noticed that my rather small number of Facebook 'friends' has two coincidences. What is the number of people required such that you have a 50% chance (or closest to 50%) that two pairs will share a birthday.

In reply to Philip:

Interesting question - to add to it, what is the number of people required for more than one to have a birthday during the week 20-27 September?

In reply to Tall Clare:

Assuming that is the week of yours. Do you mean the number of friends for a better than 50% chance that one is in that week?

The answer to that is 36 friends. At 36 friends there is a 50.2% chance that one of them has a birthday in the 1 week you have specified.

Interestingly at 35 friends the chances of one having a birthday +/- 3 days of your own is less than the chances of any two of you having the same birthday. I bet without doing the calculation, people would think the other way round.

In reply to Tall Clare:

If you fix a specific week then it turns out you need at least 36 friends to have better than even chances of at least two birthdays in that week. (I'm assuming that you mean 7 days? 20 - 27 Sep = Friday to Friday = eight days!).

But to have more than 50:50 chance of at least two people having a birthday in *some* week you only need 9 friends (which even some mathematicians might achieve). Or to put it another way, if you have more than 33 friends then there's only a 1 in a million chance that none share a birthday week.

In reply to Philip:

I had 3 friends (out of 150) give birth on the same day earlier this year.

In reply to Philip:

Nope, that's not the week of mine (I'm 3rd April, and I have a twin, so that automatically skews that one) - it's the week approximately nine months after Christmas. I have noticeably more friends born during that week than any other week.

In reply to Tall Clare:

The answers that we've given so far all assume that births are randomly distributed, so the answers will be the same for any given week.

In particular, these calculations don't account for twins or the fact that lots of your friends' parents like a shag at Christmas.

In reply to crossdressingrodney:


My cousins (brothers) are 23rd and 24th December. 4 years apart (but not leap years). Clearly my Uncle did something right in March only a 4 yearly cycle!

In reply to crossdressingrodney:

Here's an interesting (perhaps) article about exactly that which shows that a) births in the US at least are not randomly distributed, with September being the busiest month with 7% higher than the average number of births, and b) this non-randomness doesn't substantially affect the results of the non week-specific problem.

http://www.jstor.org/stable/2685309?seq=1

I seem to recall reading somewhere once that the birth distribution in Scandinavia was even more skewed towards the Autumn, since there's not much else to do on those long winter nights...

In reply to crossdressingrodney:


Nice!
Reminds me of
http://www.blue-straggler.net/miTunes/NeitherOfUs.mp3

Hmm the mp3 seems to have "rotted" a bit - got squeaks and jumps but kind of works

In reply to Philip:

Leap years, possibly ?

In reply to Philip:

My brother and a former housemate of mine share a birthday. 2 days after my cousin and step sister. I did once know a girl called Kerry who shared my birthday. That was a bit weird.

In reply to Philip:

To answer your original question:

If you have at least 36 friends, you have better than even chances of having at least two pairs share a birthday*.

As it turns out, regardless of how many friends you have, there are *never* better than 50:50 odds that exactly one pair share a birthday. The best you can do is 28.0% with 39 friends.

* For the pedants: this happens to be true whether or not you consider a triple-birthday coincidence (a, b, c) to count as three distinct birthday pairs (a, b) and (a, c) and (b, c).

In reply to ceri:


I once met a girl called Karma who shared my birthday (she also shared my cringing at her name, bemoaning her befuddled hippy parents )

In reply to Blue Straggler:

That's beautiful. I just realised I've never heard their radio stuff before, so thanks for that.