Pick two points at random on a circle and draw the chord connecting them.
Pick two more points and connect them with a second chord.
What is the probability that these chords intersect?
This is possibly too easy, but instead of thinking of it as 2 points chosen and then two more points chosen, let's just think of it as 4 points chosen. Once I have four points, there are only three ways to draw 4 chords: one way is an x, and the other two are semi-parallel segments.
Well...then, the probability that the chords intersect is 1/3.
I've been chewing on this one all afternoon, and this answer seems to simplistic, but--as was pointed out in the comments--it is difficulty 1.
solution, maybe
