Birthdays

It is quite surprising to most people to learn that if one is in a room with a total of 23 (or more) people, at least half the time, at least two people in the room have the same birthday. (We assume that all birthdays are equally likely, i.e. the people are a random assortment). Below, we tabulate the probabilities of that event occurring, namely a birthday match, in a room full of n people, as n varies from 6 people in the room to 61 people.

# of people, followed by the probability that there's at least one day with at least two people having the same birthday

It is even the case that the matches will typically occur several times; that is, there will be several days on which at least two people share a birthday. For this to occur at least half the time, namely that there are at least two days where at least two people have the same birthday, you need at least 36 people in the room.

# of people, then probability that there's at least TWO days with at least two people having the same birthday

Finally, a graphical rendition of the above information:

More graphics? Questions? Contact Rick Kreminski (kremin@boisdarc.tamu-commerce.edu)

This document created October 19, 2003