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Re: Marilyn, again



As Doug Craigen and Jerry Hester point out, the answer does depend
on the distribution of birthdates which is taken (incorrectly) to
be flat in the standard solution. Richard Grandy argues that
these deviations are likely to be relatively small and that the
low probability days may somehow balance out the high probability
days.

I too would expect the actual distribution of birthdates to have a
relatively small effect on the calculation, however, my intuition
agrees with Leigh's in making me expect that *any* deviation will
*only* make the probability of identical birthdates *larger* (and
result in even more "virtual certainty.") Clearly, in the extreme
case that everybody is born on the same day, the probability of at
least two having the same birthdate in any group of 2 or more is
100% and I can't see any competing factors that would lead to a
complicated enough dependence on the distribution to result in a
minimum probability for any distribution other than the flat one.

I was, however, more interested initially in the response to
Marilyn's answer which I do disagree with. As Mark Shapiro points
out, 97.3% (I get 97.0% while Richard gets 97.5%) would indeed be
called "a sure thing" in many situations including, I dare say,
this one. (On the other hand, a 97% survival rate after taking
two aspirin for a headache might be thought of in distinctly
different terms.) In any event I see no reason to think that the
reader engaged in an "erroneous extrapolation" of the 23 person
result which might be expected to lead some to believe that
*absolute* (not virtual) certainty occurs with 46 (not 50) people.

John
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