A formula to accompany the Birthday Problem Let's look at the
probabilities a step at a time. Running this through a computer
gives the chart below. Notice that a probability of over .5 is
obtained after 23 dates! - For one person, there are 365
distinct birthdays. - For two people, there are 364 different
ways that the second could have a birthday without matching the
first. - If there is no match after two people, the third person
has 363 different birthdays that do not match the other two. So,
the probability of a match is 1 -
(365)(364)(363)/(365)(365)(365). - This leads to the following
formula for calculating the probability of a match with N
birthdays is 1 - (365)(364)(363)...(365 - N + 1)/(365)^N. Notice
that the probability is above .9 before the sample size reaches
even 45. Also, take a look at Lionel Mordecai's MathCAD
programs. The algorithms are in an RTF file. It includes a nice
graph of the output. He uses the programs in his statistics
class. Return to the Introduction. Send comments to George