Psychologists and statisticians often illustrate people’s poor grasp of probability by asking….How many people do you need in a room to have a 50% chance of any two of them sharing the same birthday?
According to the laws of probability the answer is surprisingly small, but is it correct? Let’s put this world famous problem to the test…..
According to the maths, you only need 23 people in a room to get a 50% chance of any two of them sharing a birthday. Squash 57 of them in the same room and the probability of a match apparently rockets to about 99% (for the theory, see here).
Let’s put this theory to the test….
First – if you are reading this, please join in, otherwise the numbers get all screwy.
Second, here is my birthday….17 September (no need for a big present, a card containing money will do)…..
Third, if the first person to read this also happens to be born on the 17 September then they should add a comment saying ‘Match! (17 September)’. However, if they are born on another day they should simply write their birthday (e.g., 12th March). There is no need to add the year you were born.
Fourth, the next person then looks at the two dates (17 September and 12 March) and, again, if they are born on one of these two dates (e.g., 12 March), writes ‘Match! (12 March)‘. If not, they add their birthday to the list.
And so it goes on…..if ANY of the dates already listed matches your birthday then you write ‘Match!’ and say which date it is. Otherwise you add your birthday to the list.
According to the theory, we have a 50% chance of a match with just 23 people and a 99% chance with 57. But will our experiment support the theory?
OK, step forward and share your birthday (and encourage your friends to do the same – we need lots of people for this to work)…..everyone have just one go and no lying!