[noahc]

I just tried this on my brothers account. It lets me guess at his security question and then kicks me to a page that basically says that they currently don't support password recovery without knowing the answer to the security question.

[tshtf]

Apparently it's a feature where you can't update your security question either:

We want to make sure that your account and the information in it stays safe, so once you set up a security question on your account there’s no way to update it. Sorry for the inconvenience.

https://www.facebook.com/help/?page=227159377299846