Hi everybody,
the other day I was watching a programme on the BBC, and someone said you only need to collect 23 people at random to have 50% chances that at least 2 of them have the same birthday.
So I set about calculating this probability for a generic N (number of people), and found this formula (leap year not considered):
It seems to work, and it predicts 99.9% chances of at least 2 matching birthdays with as little as 70 people, and certainty (1) for N>=366.
However, as the corresponding plot looks sigmoidal, my question is whether there is a nicer formula, where there is no index i.
Thanks
L