Thank you Peter, could you (or anyone) explain how you got to 33%, please?
Assuming that the question is asking "if you stood the stick up on its end and let it fall over, what are the odds that any part of the stick lands outside the circle?" the answer is 66.67%. Explanation: Draw a circle, then draw another identical circle such that the circumference passes through the center of the original circle. Mark the points where the circumferences of the two circles overlap. You can draw two equilateral triangles joining the centers of each circle to each other and to these two points, which marks the boundary within which the stick must fall to remain fully in the original circle. You will notice that these two triangles represent 2/6 of a hexagon that can be drawn inside the second circle. Therefore, the probability of the stick falling completely inside the circle is 33.33%, and the probability that any part of the stick lands outside the circle is 66.67%