I completely agree with this and always find it instructive to examine wording thoroughly when posing problems or solutions. However, I think you could come across more likably by offering a better wording yourself in your comment. I'll have a shot at it:

"Given two random points inside a square, what is the probability that the center of the square lies in the circle formed by taking the points as diameter?"

I'm not happy with my opening clause there though, possibly because I omitted to explicitly state the distribution (that is, uniform - all points are equally likely). It seems there is a convention to assume uniform when no other information is given, but I still don't like "random" there. What would be your wording?