# Expectation of differences between arcs on a circle

Consider a circle with a circumference of $$n$$. On this circle, I define two arcs of length $$k, $$A_1$$ and $$A_2$$. The centres of the two arcs are uniformly distributed on the circle.

Let $$\Omega_{1}=A_1 \setminus A_2$$ and $$\Omega_{2}=A_2 \setminus A_1$$ such that the length of $$\Omega_1 \cup \Omega_2$$ is $$2k$$ minus the overlapping part of the two arcs.

What is the expectation of the length of $$\Omega_1 \cup \Omega_2$$?