An intersection of geometry and combinatorics

Discrete Mathematics Level 4

Consider a square with vertices \((0,0), (0,1), (1,1)\) and \((1,0)\). Choose a random point within the square and draw a line segment from it to \((0,0)\). Next, choose a second random point within the square and draw a line segment from this point to \((1,0)\).

The probability that these two line segments intersect is \(\frac{a}{b}\), where \(a\) and \(b\) are positive coprime integers. Find \(a + b\).

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 4 million people

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