Birthday

Suppose a trampolining club has 10 members present on a given Tuesday night. What are the chances that two of them will share a birthday the following day?

Actually, that isn't really the question. My birthday is already known to be the 18th of May, so that's a precondition. What are that chances that any of the remaining 9 present bouncers have the same one?

Not knowing the ages of the others, we must take into account the possibility that they were born on a Leap Day, so the chances of any one of them being born on May 18 should be 4/(365 * 4 + 1). If we were dealing with a longer timescale, there'd be the issue of non-leap century years to consider, but you'd've had to have had a fucking long bouncing career for that to be an issue. To the best of my knowledge, all bar one of my fellow trampolinists are younger than me, and that one's age is a long way short of the 105 that would be needed to invalidate the rule that every fourth year is leap.

So, a naïve analysis suggests that the likelihood is 9 * 4/(365 * 4 + 1), or about 2.5%. I'm too drunk and tired to be able to say whether this is indeed correct; these questions are usually framed in a rather different way, with a lot more left to chance, and those frameworks don't apply. And this is assuming the sample space is uniform, which may not be the case. Perhaps people born in May have a greater tendency to bounce?

In any case, it is also Kate's birthday today, so Happy Birthday, Kate! We two post-trampolining compleannists, along with various others, went on something of a celebratory spree, hence the late and bladdered posting. It served a purpose.

Now, I must crash out. See y'all back in the land of the living.

xox
Posted by matt at May 18, 2005 04:01 AM