Category Archives: Probability

Geometry Probability – 4

Posted on February 2, 2025 by kevin

Let $D$ is an interior point inside equilateral $\triangle{ABC}$. Find the probability that the line segments of $AD$, $BD$, and $CD$ are the side of: (1) a triangle, (2) a right triangle, (3) an obtuse triangle, and (4) an acute … Continue reading →

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Geometry Probability – 3

Posted on September 18, 2024 by kevin

Two points are randomly and uniformly selected from the interior of a circle. The center of the circle and the two points joined together form a triangle. What is the probability that the triangle is acute? Click here for the … Continue reading →

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Geometry Probability – 2

Posted on August 5, 2024 by kevin

An iron rod of $1$ foot long is cut into three segments with random length. (1) What is the probability that the three segments form a triangle? (2) What is the probability that the three segments form an acute triangle? … Continue reading →

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Probability Challenge 2022/08/29

Posted on August 29, 2022 by kevin

A frog can randomly jump exactly 1 yard away in any random direction constantly. (1) What is the probability that the frog is within 1 yard away from its starting point after 2 jumps? (2) What is the probability that … Continue reading →

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AIME II 2021 – Problem 8

Posted on December 24, 2021 by kevin

An ant makes a sequence of moves on a cube where a move consists of walking from one vertex to an adjacent vertex along an edge of the cube. Initially the ant is at a vertex of the bottom face … Continue reading →

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