The Three Musketeers in a Semicircle Problem
Yet Another Probability Brain Teaser Which Requires Geometric Understanding. Give It a Shot and Match With Mine.
Image credit: Me
I came across this interesting problem on which my seniors were brainstorming late at night. It requires a bit knowledge of continuous random variables in probability and little bit visualization capability.
The problem goes like this…
There are three musketeers who stand on a circle randomly, which follows Uniform(0, 2πr) independently where r is the radius of the circle. They can help each other if they are close enough in case of a sudden attack by the enemies. Find the probability of them lying on the same semicircle.
Read my detailed solution at: The Three Musketeers in a Semicircle Problem
Rishi Dey Chowdhury
Master of Statistics
My research interests include Artificial Intelligence, Quant Trading, Deep Learning and their applications in Market Microstructure, Computer Vision and NLP.