It was my birthday earlier this week and in the evening I went to choir. Every few weeks on average this particular choir sings ‘Happy Birthday’ to one of its members, and I wondered whether this happened for any choir member who went to a rehearsal on their birthday, or just for those who are on the committee or help out in some other way.
The formula above, supplied by a mathematician friend, tells you how many different birthdays you might expect in a group of N people. For 100 people it’s about 88. Another mathematician friend ran a numerical simulation which agreed with this. (I know it was that time of year, but let’s ignore February 29th for this calculation.)
As there are about 100 people in the room at a typical choir practice (such as yesterday’s), and as far as I know no sets of twins in the choir, the formula above gives a chance of just under 1 in 4 that it is the birthday of at least one of them. Of course if it is in fact your birthday, you are more likely to give choir a miss that week and spend the evening with your family or down the pub. That suggests that ‘Happy Birthday’ might get sung about one week in six, which seems about right – and implies that all choir members are entitled to be serenaded with it on the appropriate day.
What actually happened was that we were invited to sing ‘Happy Birthday’ – to an alto who shares my birthday. I quickly piped up that it was mine too, so both our names were included. Although as a relative newcomer most people either didn’t know mine at all (it wasn’t I think announced) or thought they did, but in fact didn’t.