In this paper we consider two independent and identically distributed lines, which intersect a planar convex domain D. We evaluate the probability P, for the lines to intersect inside D.
Translation invariant measures generating random lines is obtained, under which P achieves its maximum for a disc and a rectangle. It is also shown that for every p from the interval [0,1/2] and for every square there are measures generating random lines such that P=p.

Ara Gasparyan

Proceedings of the YSU, Physics & Mathematics, 2015, Issue 2, Pages 3–6

Random line, convex domain, translation invariant measure