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The Friday Fillip: Birthday

Posted By __Simon Fodden__ On November 9, 2012 @ 7:30 am In __Miscellaneous__ | __Comments Disabled__

Chances are really good that a few of you among the thousands (yes, thousands) reading this are celebrating a birthday today. It can’t be a dead cert, of course, because there’s no law of nature that requires that anyone in our readership be born on a ninth of November. There is, though, a law (or maybe a regulation) of nature that seems to dictate that approximately the same number of people get born every day. And that being the case, I should be able to estimate the chances that some of you will indeed be blowing out candles today.

Trouble is I’m the next best thing to innumerate. But let me essay this problem anyway and invite correction, otherwise known as help. We have to assume that the same number of people are born each day, and that there’s no bias as to whether a particular birth date influences if you’re likely to read Slaw or not. Assuming further, then, for argument’s sake, that 6000 people read Slaw each day, it ought to be a fact (i.e. not statistics but “mere counting” as a statistician I know once called it) that at least 16 Slaw readers (6000 รท 365) will be blowing out candles today.

Of course, all of this assuming — from the assumption that our population of readers is a true representation of the whole population and on to the assumption that each day’s crop of kids is the same size — has to produce wobbly results. Which is where probability and statistics come in.

And when it comes to those two and the topic of birthdays, the commonest get-together is a poser that goes by the name of the birthday problem. Simply put, the question is this: what is the size of the group necessary to make the chances 50-50 that two people will have the same birthday. I won’t keep you in suspense. The answer is 23. (I know. In its seeming arbitrariness, it’s like the answer to the question of what is the meaning of life, the universe and everything ^{[1]}, which happens, as I’m sure you know, to be 42.) All is explained really well in a New York Times Opinionator piece ^{[2]} from last month by Steven Strogatz. Thanks to one of the leads in his article, I went to the WolframAlpha page for the “birthday problem calculator” ^{[3]} where there’s a device that lets you input the number of people and that then kicks out the probabilities that two (or three) of them will have the same birthday. (e.g. 40 people gives you an 89% likelihood that 2 will have the same birthday.)

I’ll leave you with Beatle Paul McCartney’s performance of the Lennon and McCartney song, *(They say it’s your) Birthday*, and my wishes for many happy returns of the day. You know who you are.

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URLs in this post:

[1] what is the meaning of life, the universe and everything: **https://www.google.com/search?num=100&hl=en&newwindow=1&safe=off&tbo=d&q=answer+to+life%2C+the+universe+and+everything&oq=answer+to+life%2C+the+universe+and+everything&gs_l=serp.3..19j0l7j0i5l3.71600.71600.0.73289.1.1.0.0.0.0.393.393.3-1.1.0.les%3B..0.0...1c.2.gmoFN6Xc_qE**

[2] a New York Times Opinionator piece: **http://opinionator.blogs.nytimes.com/2012/10/01/its-my-birthday-too-yeah/**

[3] the WolframAlpha page for the “birthday problem calculator”: **http://www.wolframalpha.com/input/?i=birthday+problem+calculator&a=FSelect_**BirthdayProblem--&f2=23&f=BirthdayProblemWithLeapYear.n_23**

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