I frequently use the birthday problem to demonstrate that people can be very poor at estimating probabilities. My classes are usually 25-30 people, so I know I have a better than 50% chance of having two people in the room with coincident birthdates.I was teaching a crowd of about 20 people in GE's Crotonville training centre, so I was worried that it might not work. We went around the room of people from all over the planet and found a pair after asking 6 people. I thought I had made my point, but the class wanted to keep going. When we finished the room we had 4 pairs of people with coincident birthdays.The usual result is that in a statistics class of 364 people, no one will have coincident birthdates.We all are plagued by the tails of distributions.

Is there no end to Aaron's set of databases of useful information. Five different but similar Sherlock Holmes quotes last week, 10,000 birthdays of famous people the next. What are the birthday biases of famous people, and are they any different to those for us mere mortals?

More musings on birth date clusters...My wife and my mother (two different people before anybody wilfully misinterprets) have the same birthday - different years of course. It did not take me 22 girlfriends to find one with a matching birthday. And I wouldn't recommend it as you either cause resentment from somebody or end up hosting a double size party. My Dad told me that in Britain around the time he born (1943), there were clusters of babies born in March, as it was possible to claim a whole year's tax allowance for a child born during the tax year, which ended at the start of April. He was one of that cluster, though his probably wasn't such a large cluster as it was during the second world war. Of course the post war baby boom clusters births in particular years (My Mother - 1946), as do second (me) and third (my kids) generation baby boomers. During the 1997 UK election, the Labour party was campaigning saying it would deliver smaller infants school class sizes within five years. I wondered how much of the delivery (or not) of that pledge was due to something they knew about birth rates. My daughters' school had more places in its reception classes this year than it had children from its catchment area. Is it true that there are clusters of births nine months after power outages? Was there a millenium baby boom? Are the UK Government quietly dropping their class size pledge because of it.

I have heard of "Sept 11" baby boom. It seems many US young people felt the need to share affection after that dreadful event and the result became clear in 9 months.Now the twist to the brainteaser question. Will all these well reported events causing birth-dates to 'cluster' & not remain fully random, increase the size of class required to 0.5 prob of shared birthday or will it reduce the minimum size ?

If you have a cluster effect, it would definately increase the probability of a pairing for a given size group. Or to answer your question, you'd need less people to have a 0.5 chance of a pairing.

I guess we should be modelling the 'theta time'...the 9/11 baby boom thing is a mystery to me - the event caused me to lose my apartment... and I would say that staying with an ex-Cantor MD for the month that I was looking for a new one didn't exactly 'create the mood'. Though maybe it could be argued that we might have been inspired to make up for lost time... guess I missed an opportunity.

CSParker was luckier than he knows (or unluckier, come to think of it, at least if dating is a pleasure). It would take 253 dates with randomly selected partners to have better than a 50% chance of getting one who shared a birthday with your mother. On average there would be 87 pairs of those dates who shared birthdays with each other.The most impressive documented birthday clustering effect of famous versus ordinary people concerns professional soccer players. Those with birthdays such that they tend to be older than their cohorts on youth teams are almost twice as common as those with birthdays just before the cut-off. If age at September 30 determines team membership, for example, kids born in October are far more likely to become professional soccer players than kids born in September.The reason appears to be that the dropout rate from the "professional track" is very high, about 35% per year. The vast majority of those dropouts are genetically unqualified to ever become professional-caliber players, but a few could make it if they stuck it out. However the relative discouragement from being a year younger than most of the players tips about half the kids who would otherwise persevere into early retirement.The effect is less pronounced in other sports. I think part of the reason is it's easier to reenter the professional track in most sports, because the skills are more general. Big, strong, fast, disciplined, graceful people with excellent reflexes and eyesight can do well in most sports. They can hone those talents and learn the specifics of basketball, American football and other sports in their late teens. But it's almost essential for a professional soccer player to learn key skills much earlier in life. The other sports for which that is true, such as golf, tennis, swimming and gymnastics, are not so rigid in age classification.There is a similar effect in overall achievement related to academic calendars. The oldest kids in their school classes do better than the younger. Here the effect seems less due to dropout than confidence.It is definitely true that there are surges of births after a storm that keeps people indoors or dramatic event. Also, women are more likely to conceive in bad weather (winter in the temperate climes, rainy season in tropical, year round in Scandanavia) than good. Conceptions are unrelated to the phase of the moon, but births have a measurable lunar cycle peaking at the full moon (however this does not affect birthday clustering because the full moons dates change every year).The clustering increases the chance that a given number of randomly-selected people will have a shared birthday, but not by much. In my data sample (all these data samples are easily found on the Internet, by the way) it was almost exactly offset by the leap day effect, which lowers the probability.

Aaron clears up a number of issues:1. Why neither my wife nor my mother are not professional footballers (that's what we call them over here). Their birthday is August 29th, which is almost as young as you can be in a British academic year. Academically, the younger Mrs Parker (my wife, before you ask) bucks the trend as she has a pretty good degree. She was a late bloomer in secondary school though. 2. That soccer is a king among sports, as it requires skills that are either innate or learnt very young. An anecdote on this comes from the former England player and manager Glenn Hoddle, now manager of Spurs (natch). When very young, he was playing catch with a ball on the beach. Well, his parents thogh he was playing catch, young Glenn was trying to kick the ball all the time (doubtless with his shirt untucked and shorts pulled a little too high for decency). This game was spotted by a football team scout who told his parents that they already had a special talent on their hands. 3. That the England football teams relative lack of success is due to genetics and not a failure of coaching, management or the players - can't wait to see that excuse be used. Could Aaron please provide similar evidence to explain the current England cricket team's situation?

I've always had the suspicion that birthdates clustered around the Aug/Sep/Oct in the western world because of the associated holiday season at end of Dec/beginning of Jan.Can someone supported or disprove this hypothesis by data please?

How about a comparison of the frequency of birthdates in mid november pre and post the incorporation of Hallmark??

<blockquote>Quote<hr><i>Originally posted by: <b>csparker</b></i>3. That the England football teams relative lack of success is due to genetics and not a failure of coaching, management or the players - can't wait to see that excuse be used. <hr></blockquote>And maybe this can also explain the fact that the Dutch national team always fails to score with penalty kicks... always...

See this link. (You might need to download some mathematica viewing software, from the same website; it is free.)

As many here have already alluded, this problem is a classic. It even gets cited in the popular press:http://www.csicop.org/si/9809/coinciden ... NCE.htmlIt might be reasonable to assume anyone who has heard the problem might have memorized "23", even if they don't remember the solution.However, in terms of "n" how many digits of precision are required to calculate an answer accurate to at least the first digit? Another angle on this same question is to ask what is the numerical max "n" for which MS-Excel is able to accurately (1 sig fig) calculate this probability? MS-Excel reaches its limits surprisingly soon. Please also express the answer in terms of "n" rather than just a numerical answer for one particular "n." Related to finding this answer is to determine what is the max factorial which Excel can calculate. Again, surprisingly small.