2015; Physical and Mathematical Sciences, 49(2 (237): 3–6
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PAIR OF LINES AND MAXIMAL PROBABILITY

Ara Gasparyan*

Received: 2025-02-11 · Published: 2015-06-12

© 2015 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
PAIR OF LINES AND MAXIMAL PROBABILITY
Author
Ara Gasparyan
Published
2015-06-12
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.46991/PYSUA.2015.49.2.003

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.
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