Staying in the triangle

Discrete Mathematics Level 4

Three points are chosen uniformly at random from the boundary of a square and a fourth point is chosen uniformly at random from the interior. The probability that the 4th point lies in the triangle formed by the other 3 points can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b?\)

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.