PAIR OF LINES AND MAXIMAL PROBABILITY

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Submitted: 2025-02-11; Published: 2025-02-11

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Abstract

In this paper we consider two independent and identically distributed lines, which intersect a planar convex domain D. We evaluate the probability PD, for the lines to intersect inside D. Translation invariant measures generating random lines is obtained, under which PD 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 PD = p.