Birthday Matcher Mission Statement:

The sole purpose of the Birthday Matcher social networking site is to enable and empower its members to find and build unique meaningful global friendships and connections with people of other cultures who share their exact same birthday (day, month and year). We envisage a global community where members can create enjoyable, meaningful friendships with other members who have led parallel existences, all be it in different locals and under widely diverse social and economic circumstances. We firmly believe that these friendships will greatly enhance cultural understanding, tolerance, appreciation and respect of the world we all live in. The Birthday Matcher social networking environment has been specifically designed to promote the honest exchange of real life experiences between like minded individuals. These experiences will hopefully enlighten, elucidate, educate, encourage and empower people with a wealth of previously untapped knowledge, which is generally unobtainable in the normal course of their lives.

The Birthday Problem

What are the odds of someone you meet has the same birthday (day, month, and year) as you? Let us assume that you are 35 years old, and the person you meet is a random person in England between 20 and 50 years old. Then using the age distribution data for England in 2001 (available from http://en.wikipedia.org/wiki/Demographics_of_England_from_the_2001_United_Kingdom_ census), we obtain that the chance this person was born in the same year as you is

where the numerator is the proportion of individuals in England the same age as you, and the denominator is the proportion of individuals in England between 20 and 50 years old. Notice that I have taken the proportion in the age group 45-59 and multiplied that by 6/15 to obtain an approximate proportion in the age group 45-50. The denominator will change if you change the age group of the person you meet, whereas the numerator will change if you change your own age.

The above gives an estimate for the chance that someone you meet is born in the same year as you, which one can multiply by 1/365 to obtain the chance that the person you meet was born on exactly the same day, month and year as you:

or approximately 1 in 10361.

Finally, if one multiplies this by the number of person you meet, you will arrive at the odds of meeting someone with exactly the same day, month and year of birth as you. If we take a figure of 100 (which according to certain web sources, is the average number of friends a person has), then we arrive at a figure of approximately

.00965,

or approximately 1 in 104. The figure of 100 is of course arbitrary. The figure we should use here is actually how many among those you meet are likely to tell you their birthdays.

Solution provided by Feng Yu, University of Bristol, 2009