On a circumference of a given circle with a radius R two random points A & B are independently chosen.
What is the probability of AB being less than R ?
For convenience create a coordinate system with the origin at the center of the circle and (1,0)=A
B is at some angle from -180 to 180 from A with uniform probability. AB is only closer than R if the angle is between -60 and 60.
Thus the probability is 120/360 = 1/3.
Posted by Jer
on 2018-04-26 09:50:49