I Want Answers!

A couple weeks ago I posted my list of all Pixar features from top to bottom.  And I wondered how likely it was that someone had the same preferences.

A friend much better at math has helped me out.  I won't show all the work he did, but I'll give you the results.

First (and this is the easiest thing I asked), the odds that someone in the world would make the same list is about 1 in 50,000. That's because the number of permutations of the film list is 17!, or about 350 trillion.  Now figure there are about 7 billion people in the world, each one making a list, and divide that into 350 trillion and you get a 0.002% likelihood of a match.  (This is assuming all titles are as likely to be in one slot as another.  This is not the case, but was used for ease of calculation.)

The more interesting question, I think, is how many people would you need to make lists before it's more likely than not that you can find two that match.  This is a variant of the "birthday problem"--where probability shows us that 23 random people are more than 50% likely to share at least one birthday, and 70 people have a 99.9% probability of having at least one match.

For my problem, with 350 trillion permutations, it turns out if you've got a bit more than 22.2 million people, you've got a better than even chance that at least two have the same list.  Though it's my guess, with certain titles so much more popular than others, that you'd need less than a million lists--perhaps somewhere in the thousands or tens of thousands--to have a 50%+ shot at a match.