On the circumference $x^2+y^2=1$ one randomly chooses (uniformly and independently) $3$ points. These points split the circumference, forming $3$ arcs.
What's the expected value of the length of the arc which contains the point $(1,0)$?
Is there any quick way to solve this? I kind of already used some symmetries but it seems too complex to me. (It's supposed to be an easy exercise, so maybe there's some clever thing to consider.)