great explaination. its helping. i’m doing a math project about diehard randomness test… can you help me to understand of the test that is called birthday spacing test?
Your formula P(different) = e to the power of - (2223/2365) is incorrect. If you punc that in to a TI-83 plus, you’ll get zero as an answer. You need 2223 in it’s own bracket and the same for the 2365. The division sign would stay outside of the two brackets, in the middle. It should really look like this: P(different) = e to the power of - (2223)/(2365). It took my forever to understand what was wrong with the equations until I finally clicked ‘very close’ and say the other calculations. Haha. Hope this helps anyone who was as confused as I was. I thought my TI-83 was broken! (:
Umm, I’m not a mathamatician… so please excuse me if this is a stupid comment. I understand the principle behind the calculations. I even agree that they are correct. However, one thing which seems to me to be incorrect is the assumption that birthdays are prefectly evenly distributed throughout the year. An equal weight (likelyhood) is being assigned to each day of the year. I think in reality that there are far more birthdays at certain times of the year, and therefore on certain days of the year (9 months after xmas, valentines day, etc.) I don’t see anywhere where this is being included into the calculations. Can you explain? Thanks.
@Caro: Great question! Yes, you are absolutely right – we currently assume that birthdays are distributed evenly. To simplify the problem, we ignore the possibility that birthdays could have a certain spread – realistically, it may be slightly more than 23 birthdays to account for this. But, I doubt the real distribution is very much different from the ideal one (certain holidays only celebrated in certain countries, etc.) so it might all average out reasonably. But that’s a great point to bring up.
first i got a bit confused
dat wat d helll is birthday paradox
but after reading dis
it is damn easy
thank U
very much
In our retirement village we have a birthday book, which contains about 80 names. The birthdays are read out each month to a gathering of about 25 people. If a certain person is there the same time as me,we have a match. Otherwise. NO
Please stop confusing people. Let’s stop the confusion all over the world with this annoyingly wrong principal. I don’t mean computatively wrong. I mean, it is wrong to call it the birthday principal. It is a number principal with 365 set numbers principal.
This problem has been confusing people for the longest time, because no one will explain that it does not do what people think it is supposed to do. Which is calculate the odds that 365 people in a room will find someone else with their birthday.
The problem itself is actually very easy to understand. Even I can understand it and I never learned any advanced math. The equation is cheating. It has nothing to do with any applicable birthdays. There is no reason to delete each match after it is made.
This is not a paradox. This is a simple math problem, and its title confuses people into thinking that something impossible is happening, when its not, they are just being confused by an incorrectly named title of a principal.
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Old thread, but still interesting. Here’s a simpler way of doing it - look at your Facebook birthdays, how many shared birthdays are there?
Indeed, export your friends birthdays, pick a sample of 23, and see if they match up - quite surprising!
LOL! At first I thought about my classroom, and instinct said how unlikely it was that two people had the same birthday, and then I realized we had a set of twins…
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Your equation right after you mention “the multiplication looks pretty ugly” looks like it could be computed using factorial(!) notation, which many scientific calculators have:
1*(1-1/365)(1-2/365)…(1-22/365)=
1(364/365)(363/365)…*(343/365)=
365!/{(365-22)!*365^23}
But 365! is likely too big for many calculators to handle.
[…] mental math trick involved is known as “The Birthday Paradox.” You can skip directly the more technical explanation if you prefer. The question wasn’t about whether or not two people had one particular […]
@gavin I went ahead and created a Facebook app to show the Birthday Paradox with your friends: http://apps.facebook.com/thebirthdayparadox/