Birthdays

I got randomly solicited by telephone surveyors today (something about my tastes in alcohol). In the course of it, the telephone interviewer asked me what my birthday was. I said 23 December.

"Wow," she said. "You're the second person I've talked to today who had that birthday! And I've only called about twenty-something people!"

It's not all that surprising, though. In any randomly chosen group of twenty three people, your odds of finding two with the same birthday are better than 50%.

Much like the Monty Hall Paradox (not actually a paradox), this seems counterintuitive when you first hear it, until you start thinking about it backwards. For example: what are the odds that person 2 has a diffferent birthday from person one? 365 in 366, right? Okay, so then what are the odds that as well, person 3 has a different birthday from the first two? And then that person 4 has different birthdays from the first three? And so on, through to lucky number 23.

It took me ages to explain to the phone interviewer, though. I'm not sure we ever did finish the survey.