Re: real world birthday problem.


pauldepstein@xxxxxxx wrote:
> 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.)

You think? Not very scientific.

>
> 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.

Calculations based on the assumption of fair distribution. Why does it
surprise you that you get the wrong answer when your assumptions
are wrong?

>
> 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.

Wildly wrong? How wildly wrong? Does the weekend adjustment result
in a whole person, i.e., do you actually need 24 to find a duplicate?

> 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.)

When the teacher queries the 30 students in the class and finds a
duplicate, he says "See, I was right."

When he queries the 30 students in the class and finds no
duplicate, he says "See, I was right."

I don't see any problem here.

>
> This is very conjectural, since I haven't seen any real-world analysis
> of the birthday question.

Because nobody cares.

>
> Any comments?

Yeah, why don't you get a grant and build a machine to study coin
flipping.

Oh, wait, that's been done already.

>
> Paul Epstein

.

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