On an \(n \times n\) square grid, two vertices are chosen at random and a segment is drawn connecting them. As \(n\rightarrow \infty,\) what is the probability that the segment does not cross any vertices of this graph besides the two chosen ones?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!