Sexy Math For Lawyers: The Birthday Paradox

Lawyers continuously deal with concepts of probability.  Understanding probabilities can be an extremely useful way to persuade, craft useful analogies, and – in some cases – either create or disprove reasonable doubt.

Probability concepts can be particularly powerful when they yield couterintutive results. One such example is the “birthday paradox.”

Quick – how many people must there be in a random group before we can expect that at least one pair shares the same birthday?

One might quickly (and correctly, albeit inefficiently) reason the number has to be 367 or less. But most would be surprised that a 99% probability is reached with just 57 people, and a 50% probability with just 23.

Note: This is NOT the same question as: What are the odds that someone in a group will have the same birthday as mine?  The birthday paradox deals with any person in a group matching any one of the others, not matching one in particular.  The chances of the latter are far less likely.

For those of you (uber-cool-in-a-math-nerd-sort-of-way) folks who are interested in the actual calculations, you can tip your hat to your old STAT101 professor here.

For those not as interested in the details, here are a few neat examples using the Academy Award winners as a proxy for a random group of people. Ask yourself if you’d have accurately guessed the number of birthday pairs:

* Of all the actors to win the Academy Award for Best Actor, 6 pairs share the same birthday.
* Of all the actresses to win the Academy Award for Best Actress, 3 pairs share the same birthday.
* Of all the directors to win the Academy Award for Best Director, 5 pairs share the same birthday.