Monday, December 18, 2006
The Birthday paradox/problem
Did you know that if you are at a party with 23 people attending, then the probability that two people will share birthday is more than 50%!
I sometimes use this example as a way to show people that our intuitive reasoning with numbers can be quite wrong, and it really works, people shake their head in disbelief when I tell them this statistic. How can this be? To illustrate imagine that there are two people attending a party. There are 364 ways in which the second person will not have the same birthday as the first person. For the third person there are 363 days which are still not occupied. The formula that we get is that the probability that at least two people share the same birthday when there are three people attending is 1-(365*364*363)/(365*365*365) = about 0.01. If you do the same calculation but with 23 people p will be just above 0.5. The general formula is: 1 - (365)(364)(363)...(365 - N + 1)/(365)^N.
Doing this calculation with 40 persons will give you a probability of around 0.9 (see graph above)! Next time you are attending a party with 40 persons or more, why not make the safest bet ever... For more information on this problem as well as a birthday generator which lets you test these claims empirically, go to "http://www.mste.uiuc.edu/reese/birthday/default.html"