Re: real world birthday problem.
- From: Hugo Pfoertner <nothing@xxxxxxxxxxxx>
- Date: Wed, 16 Nov 2005 02:09:19 +0100
pauldepstein@xxxxxxx schrieb:
>
> If I remember rightly, you can use basic probability theory to argue
> that you need 23 people in a room to get a probability of >= 50% that a
> pair in the room share a birthday.
>
> However, has this empirically been tested?
>
> Here is my guess as to what actually happens, but I think it would be a
> worthwhile topic for research if no one has actually done so.
>
> As I understand it, there is no correlation between time of year and
> birth rate in the U.S. or in England. (This is rather
> counter-intuitive to me because I would have expected more sexual
> encounters around New Year's Day and Valentine's Day, and I would
> expect levels of sexual arousal to be higher generally during the
> summer, and for this to be reflected in birthdays; but I think there is
> actually an even spread.)
>
> However, since babies are not induced on weekends, births peak on
> Mondays and are rarer on weekends.
>
> So, if the birthday question is posed to a crowd of mixed ages, the
> mathematical model and the real-world model should fit fairly closely
> since no date is more suggestive of a weekend birth than any other.
>
> However, if the question is posed to a cohort with a gap of less than a
> year between oldest and youngest (as in a high-school class), then the
> weekend factor would be huge. Hence the actual same-birthday
> probability would be much greater than the conventional calculations
> indicate.
>
> So what looks like an impressive application of pure maths to examine a
> real-world situation is a completely bogus one leading to wildly wrong
> probabilities. Ironically, the inaccurate nature of this experiment
> might lead teachers to be drawn to such class demonstrations since the
> weekend factor leads to the desired result more often than expected.
> (Desired because students are generally pleased to find the matching
> pair.)
>
> This is very conjectural, since I haven't seen any real-world analysis
> of the birthday question.
>
> Any comments?
>
> Paul Epstein
Those of you who can read German might have a look at a message I've
written on the subject in the NG de.sci.mathematik. I used the real
distibution of birth dates in the US for 1978 to run a Monte Carlo
simulation. The result was a negligible decrease of the required group
size to have at least one coincidence from 22.769 people for the uniform
distribution of birth dates over the year (assuming a 365 day year) to
22.677 people for a group of people coming from the "1978" distribution:
http://www.dartmouth.edu/~chance/teaching_aids/data/birthday.txt
See
http://groups.google.com/group/de.sci.mathematik/msg/c797104ca44b42ae
and http://www.randomwalk.de/scimath/birth2.pdf (Simulation results)
Hugo Pfoertner
.
- References:
- real world birthday problem.
- From: pauldepstein
- real world birthday problem.
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