Bill Fairchild has used some very large numbers to make his entirely persuasive
case for duplications. In fact very much smaller numbers. This problem---It
is in fact called the birthday problem---has been much studied, particularly
and all but definitively by William Feller in volume 1 of Probability theory
and its applications.
Suppose you are in a bar or pub, a place where such wagers are frequent. What
is the minimal number N of people who need to be present to make the wager that
at least two of them have the same birthday attractive?
The answer is 23. For N=23 the probability P of such a duplication is 0.5073,
making this wager attractive in the sense that one is more likely to win than
to lose it. This result is apparently counter-intuitive, and it perhaps made
easier to understand by noting that for N > 366 P = 1. The presence of more
people than birthdays makes duplication certain.
John Gilmore Ashland, MA 01721-1817 USA
_________________________________________________________________
The New Busy is not the too busy. Combine all your e-mail accounts with Hotmail.
http://www.windowslive.com/campaign/thenewbusy?tile=multiaccount&ocid=PID28326::T:WLMTAGL:ON:WL:en-US:WM_HMP:042010_4
----------------------------------------------------------------------
For IBM-MAIN subscribe / signoff / archive access instructions,
send email to lists...@bama.ua.edu with the message: GET IBM-MAIN INFO
Search the archives at http://bama.ua.edu/archives/ibm-main.html
