real world birthday problem.

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

.

Relevant Pages

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