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[Birthday Paradox Debunked-ish]
August 20th, 2007Birthday Paradox Debunked-ish
I’m a wee pedantic and the Birthday Paradox is not out of my reach. It bothers me in that it’s slightly skewed in any real life example. For those who don’t know what I’m talking about:
In probability theory, the birthday paradox states that in a group of 23 (or more) randomly chosen people, there is more than 50% probability that some pair of them will have the same birthday. For 57 or more people, the probability is more than 99%, although it cannot be exactly 100% unless there are at least 366 people.[1] This is not a paradox in the sense of leading to a logical contradiction, but is called a paradox because mathematical truth contradicts naive intuition: most people estimate that the chance is much lower than 50%.
From wikipedia
So, the standard Birthday Paradox is stated for a group of people having a match between any people in the room. I think that this is not explicitely true, and for it to be you need to add a few static environmental variables. For instance, there is not an equal distrobution of births on every day, there’s clumping in fall (due to it being nine months after the long boring days of winter) and that skews the results. For instance, if you were born in January you’d find that there would be less people born in that particular month, which makes it somewhat less likely that someone is born on the same day. In bulk, however, it’s safe to say that since there’s a mild clumping of birthdays that there’s probably a better chance that people share a birthday than stated.
If you were to randomly sample across the world it’d probably be even, given the hemispheres, cultures, et cetera. However, if you were to actually do this sort of math in any given situation you wouldn’t have the across-the-world population and you’d be subject to the local population, which would be skewed in it’s own way.
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