Facebook and the birthday paradox
This is one for math geeks with a Facebook account. I recently heard of an interesting probability problem called the Birthday Paradox. I think it was on the excellent Five Numbers series on BBC Radio 4 (or one of the 2 follow-up series). Anyway, the problem states that if you put 23 (or more) randomly selected people in a room, there is more than a 50% chance that at least 2 people will share the same birthday. The solution is not a paradox in the logical sense, it just contradicts our intuition.
Now for the Facebook link. If you have an account you probably know about the birthdays page where you can see a list of all your friends’ birthdays. I checked it the other day and was surprised to find that 3 pairs of my friends shared the same birthday. That is, before I remembered the birthday paradox and that with my 40 Facebook friends there is a 90% chance that at least 2 of them share the same birthday.
If, unlike me, you are uber popular on Facebook and have more than 100 friends, the probability should be more than 99.99996%!
(OK, I did say that this one was for math geeks…)
September 28th, 2007 at 1:09 pm
wow i have 7 pairs of birthday friends.
Including me and my mate frank (althoough i have to admit i knew about this before)
7 pairs though…
October 4th, 2007 at 3:36 pm
Note that the ‘birthday paradox’ states that they will be born on the same day of the month (so a 1 in 28, 30 or 31 chance in theory) - not “2 people will share the same birthday” (which implies day of the year).
Sorry to be such a pedant, just thought someone might get confused there.
L
October 4th, 2007 at 3:41 pm
Sorry, just found I am talking out of my arse here, and that I am totally wrong (why didn’t I press the wiki link before writing this…)
It is day of the year. Apologises all around.
October 4th, 2007 at 3:43 pm
@Liam: he he no worries. It’s a good thing you corrected yourself fast. I was ready to start a flame war.
October 4th, 2007 at 3:49 pm
I’m sure when I first read about the guy that ‘discovered’ the b’day paradox that it explained it really badly, and I’ve been wandering around giving incorrect information out at dull dinner parties all these years…
Anyway, I better go and do some actually work.
October 12th, 2007 at 1:33 am
can u read my comments because i can’t seem them
October 14th, 2007 at 4:20 am
im doin this science project you guys realy helped me
October 25th, 2007 at 5:01 pm
That’s about right - I’ve about 50-odd friends and two had the same birthday last week. The theory was brought to my attention by George Atkinson at Rocom. Spookily, we shared the same birthday, although neither of us knew at the time.
November 16th, 2007 at 3:02 am
we each should post our b-day mine is may 17
November 17th, 2007 at 9:56 pm
every time u post a commentr post your b-day
December 9th, 2007 at 12:27 am
No buddy comes on no more this is becoming stupid i feel like i m talking to myself
December 14th, 2007 at 1:36 am
i m so angry
i m so bored
i m so crazy
i m so wacky
i m so tackky
lol this is fun no1 will probaly ever read this
December 14th, 2007 at 11:08 am
@lily: I think you’re overestimating the popularity of my blog ;-). The paradox thing will start working when 23+ people post their birthday. As far as I know, we are only 5…
December 14th, 2007 at 11:14 am
@martin - overstate - never this blog *is* certainly more popular than facebook..
@lilly - 11/05
December 18th, 2007 at 11:27 pm
I had heard about this before, but never knew the numbers… it’s amazing. It is really so counter-intuitive.
So the numbers, are they based on straight probabilities, or observations?
@pete 7 pairs… out of how many friends?
@lily Nov 10
January 22nd, 2008 at 8:48 am
Sorry, I have 67 friends and no match… seems 9 months before 12 February is not a popular date for hooking up!
And oddly enough, between all of my 67 friends, there are only 2 matches.
Are you sure the paradox is right?
(I know it’s right, just my case is a special one).
January 22nd, 2008 at 8:51 am
Oops, seems I didn’t understand the paradox at first read.
It says that any two people will share a birthday, not that I would share it. So then my situation (2 matches) is completely normal.
I don’t feel special anymore
haha