Marinada '22

[lang=en] Consider a regular hexagon with side length 1. We construct a set $S$, where each of the vertices of the hexagon has a $\frac{1}{2}$ probability of being in $S$. What is the expected value of the circumference of the convex shape formed by the points in $S$? [/lang] [lang=hr] Dan je pravilni šesterokut sa stranicom duljine 1. Neka je $S$ skup vrhova, pri čemu svaki vrh ima vjerojatnost $\frac{1}{2}$ da se nalazi u $S$. Koji je očekivani opseg konveksnog mnogokuta kojeg čine vrhovi u $S$? [/lang]