Marinada '23

[lang = hr] U pravilnom šesterokutu dužine stranice $2$ (takav da su mu $(-2,0)$ i $(2,0)$ vrhovi) je odabrana točka $(1.5,0)$. Kolika je vjerojatnost da nasumično odabran šesterokut dužine stranice $1$ (i iste orijentacije kao veliki šesterokut) unutar velikog šesterokuta (svaka točka malog šesterokuta je unutar velikog šesterokuta) ne sadrži odabranu točku? [/lang] [lang = en] In a regular hexagon with side length $2$ (such that $(-2,0)$ and $(2,0)$ are its vertices) the point $(1.5,0)$ is selected. What is the probability that a randomly selected hexagon of side length $1$ (oriented like the big hexagon) inside the large hexagon (every point of the small hexagon is inside the large hexagon) does not contain the selected point? [/lang]