Speaking of probability…Happy birthday!

April 12th, 2008 at 04:31pm Pat Cunningham

Despite my having played the role of Mr. Smartypants on the subject of polling  in the post just below this one, I must confess that I don’t really understand the science of public-opinion sampling.

All I know is that reliable polling has something to do with the laws of probability.  That’s how a well-conducted survey of just hundreds of Americans can tell you what Americans in general feel about a given subject at a given point in time.

Which brings me to the fun part of what I have to say here.  There’s a certain exercise in probability that can win you bar bets in most cases if you can find any takers.

Here’s how you do it:

The first thing is to note for your mark (or sucker) that there are 366 possible birthdays, one for each calendar date and an extra one for leap years. Each person on Earth is going to have a birthday on one of those 366 dates.

Now, tell your mark that he or she can choose any 57 people at random, and you’re willing to bet any amount of money that at least two of those people share the same birthday.

The names can be chosen at random from the rolls of Congress or the Illinois General Assembly or NFL rosters or whatever.  The only requirement is that the names be chosen randomly.

In 99 cases out of 100, you’re going to win the bet.

How can this be? With 366 possible birthdays, how can there be almost a lead-pipe cinch that there’ll be a duplicate birthday among just 57 randomly-selected people?

I don’t know how.  But that’s the way it works. Moreover, there’s a 50-50 chance of a duplicate birthday among just 23 randomly-selected people. And there’s a 90-percent chance among just 41 people.

Try it at your office, if your company has at least 57 people.  Of course, if you win any bets on this thing, I’ll expect my customary 10 percent of your ill-gotten gain.

Entry Filed under: laws of probability