Exploring the Probability of Points on a Sphere
Introduction to the Problem
Dr. Johnson examined a stress ball and became intrigued by a mathematical question: What is the probability that three points randomly selected on the surface of a sphere all reside within the same hemisphere, with the dividing line belonging to one of the hemispheres?
Conclusion of the Inquiry
The answer to this question is 100%. It is guaranteed that any three points on a sphere will always fall within the confines of a single hemisphere.