What is the probability that a randomly drawn chord will be longer than the radius of the circle?
I think you need to explain how the chord was "randomly drawn" first, before calculating any probabilities.
In any case, I arrived to the answer 2/3 by two different ways:
starting with a point, just take another in the circunference
starting with a point, draw a line at a random angle, and thus determine the other point.
Of course, by "randomly" I here mean "with a uniform distribution" -- but that isn't necessary, you know...