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Consider a circle with a circumference of $n$. On this circle, I define two arcs of length $k<n$, $A_1$ 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 $\Omega_1 \cup \Omega_2$?

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