At 01:03 PM 9/17/2007, you wrote:
Hi Annette-
The general formula was postulated by Percy Diaconsis (sp?) at MIT.
To achieve a 90% probability of two events happening it is: 1.6
times the square root of the contingencies. The aproximate
contingency of a birthday (as opposed to birthdate) is 1/365 (if we
ignore leap year) therefore 1.6 times the square root of 365 =
30.57. This means that if you have 31 students in your class there
is a 90% chance that two of them will share a birthday. I often use
this as a powerful demonstration of how people often underestimate
the odds of things occuring - especially when discussing ESP. For
smaller classes it is better to have students randomly pick a number
from 1 -100. There the 90% probability of a match would occur with
only 16 participants. If you only wanted to have a 50% certainty of
a match you would only need 1.2*Sqrt C or 12 people. I'm afraid that
I don't have a reference for this as I simply remember it from a
lecture that he gave a number of years ago. He did not provide a
proof at the time & I'm not sure that I could have followed it if he did.
As a more intuitive way to do it, tell students to imagine an empty
classroom.....
One student walks in and writes his/her birthday on the board....
A second student walks in and does the same.....what is the
probability that these two birthdays are different? 364/365
A third student walks in - what are the chances there are still no
matches among the three? (363/365). What is the probability from
the start that there are no matches (364/365) * (363/365)
...and so on.....
Try it....The 50/50 point comes remarkably early....
-- Jim
---
