As many of you may know, our very own Jillian and the dearly departed Dr. Doug McLeod share a birthday (June 28th). At first glance, it may seem incredibly unlikely that two people in a relatively small research group would share the same birthday. Around the Island, such an occurrence would be referred to as a "kiracle" -- a delightful portmanteau of "Kiran" and "miracle" that refers to a sub-par coincidence that has been elevated to the level of divine intervention by a certain former post-doc.
But is this really so unlikely? Luckily, mathematics comes to the rescue to resolve this celebrated birthday paradox. Consider the case of two people. Assuming that all birthdays are equally likely [1], the probability that they do not share the same birthday is (365/365) * (364/365), or 99.7%. Correspondingly, the probability that they do share the same birthday is 1 - 0.997 = 0.3%. When we generalize this calculation, we obtain that the probability B(n) that two people in a group of n people share a birthday is given by:
Since our group consists of 23 people (including EJS, Graham, and the elusive Bob), we find that the probability that two people share a birthday is actually 50.7%. In fact, even though Doug is gone, we still have two group members that share a birthday -- Graham and Lorenz (January 11th). Truly kiraculous!!
[1] Actually, this assumption is not really valid. It seems that many more children are conceived during the holiday season, so a disproportionate number of births occur in August and September. Please draw your own conclusions and plan your conceptions accordingly.
january 11th is also albert hofmann's birthday. if i'm still dealing with celebrations at that point, i'm going to put LSD in the cake.
ReplyDeleteI am pretty sure this is a classical statistic problem set. Unfortunately, I totally returned(means "forget", if you're not familiar with Jia's grammar) the related knowledge back to the dear teacher; I am sorry.
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