Erroneous Company

Well I'm in good company making the same mistake as Johnny Carson regarding the "Birthday Paradox".  Actually I have no excuse since I have a masters degree in statistics.  Looking back at my Dec. 1 2009 Blog "A Statistician's Birthday", I made the classic mistake of statistics -  mixing combinations with specific probabilities (like Johnny Carson did on his show - Feb. 6, 1980). Consequently, I feel obligated to ReBlog and correct my mistake!

For those interested in the details read the Oct. 1, 2012 NYT article "It's my Birthday too, yeah".

Here is the summary:

(1) How many people would be enough to make the odds of a match (two or more with the same day) at least 50-50?
(2) How many people would be enough to make the odds of a match with your specific birthday at least 50-50?

The answers for 50-50 and 92%

(1) 23 people for  50%  probability              and for 43 people the odds are 92%
(2) 253 people  for 50% probability             and for 921 people the odds are 92%


So next time you are in a room of 1,000 people - announce your birth day and see if there is a match.  Maybe you will be more lucky than Johnny Carson was (actually his birth day - Oct 23 matched it was the other audience member test that failed).

PS.  Ed McMahon was pretty close with his 1000 person guess (if he was answering question #2)

PPS -  I posted this two days too early. Oct. 5th is the MOST Common Birthday.  So a good statistician would point out that certain days are not random.   Add nine months to Jan. 1  :)