John is exactly right. "Three or more people sharing a birthday" means
three or more people born on the same day of the year (i.e. three or more
people with a January 1st birthday). This does not mean three or more pairs
of people born on the same day (i.e. two born on Jan 1, two born on Jan 2,
two born on Jan 3).
Jenn
On Wed, Feb 20, 2008 at 2:31 PM, John Sheffield <jsheff at fas.harvard.edu>
wrote:
Hi Keith,
First, under the standard formulation of the birthday problem, we want the
same birthday to occur 3 or more times (your first inclination). Second,
consider the case of 6 people, where 3 pairs of people have different
birthdays (ie, 2 people share Jan 1st, 2 share March 1st, 2 share May 1st).
Your function would return a false positive here. (That was just a simple
example--this kind of problem would happen very frequently in a large
group. With 50 people, the probability of getting at least one false
positive is over 0.7...)
Hope this helps,
John
(My apologies if this went out twice--I had to resend from my FAS account.
Can someone let me know via private email if two copies of this email were
sent to the list? Thanks.)
On Feb 20, 2008 2:11 PM, Keith Schnakenberg <keith.schnakenberg at gmail.com>
wrote:
On question 2a, do we want to know the if the
same birthday occurs three
or more times, or if thee or more people share a birthday with at least one
other person? In other words, does "(length(unique(room)) < people -
1) contain the information that we need to know?
Thanks,
Keith
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