The Solution 


Answer : 1/2
Then, the factor which decides whether the chord is smaller or greater than the square root of 3 is the distance to the center of the circle. The chord is greater than the square root of 3 if and only if its distance to the center of the circle is smaller than 1/2. So, the probability is 1/2 . Here is an animation that explains the way we can get to this answer: 