Re: Marilyn, again

[rgrandy@ruf.rice.edu (Richard E. Grandy)]

> > Most of these probability calculations are based on the assumption that
> > there is an equal likelyhood of birth occuring on any given day.  This
> > is not the case.
>
> While that is quite true, my intuition tells me that any deviation from
> randomness would increase the probability of coincident birthdays rather
> than decreasing it. Am I wrong? I haven't attempted the calculation.
>
> Leigh

If we are looking at averages, ie. random sampling, then in any given
sample there will be about as many more likely birthdates and less likely
birthdates.  The result will be to make the difference, if any, from
equiprobable outcomes very small.  The calculation gets complicated
quickly, but I did an example where you have people choose numbers from
1-10 inclusive.  Each person chooses sequentially in ignorance of the
previous choices.  On average after four choices there is about a 50-5-
chance that two have chosen the same number, assuming equiprobability.  I
then did the calculation assuming that one number had .15 probability of
being chosen, and that one had probability  .05 (more extreme variation
than you have in birthdates), and the probability of having a match after
four choices differed only in the third decimal places.

Richard Grandy
Rice University
Philosophy