Question 12356 – TIFR PHD CS & SS 2015

Consider a circle with a circumference of one unit length. Let d < 1/6. Suppose that we independently throw two arcs, each of length d, randomly on this circumference so that each arc is uniformly distributed along the circle circumference. The arc attaches itself exactly to the circumference so that arc of length d exactly covers length d of the circumference. What can be said about the probability that the two arcs do not intersect each other?

Correct Answer: C