Spinning Spherical Target: Probability for Three Marksmen to Hit on the Same Hemisphere | CE Board Problem in Mathematics, Surveying and Transportation Engineering

Date of Exam

November 2016

Subject

Mathematics, Surveying and Transportation Engineering

Problem
Three marksman simultaneously shoot and hit a rapidly spinning spherical target. What is the probability that the three points of impact lie on the same hemisphere?

A. 0	C. 1
B. 1/2	D. 2/3

Answer Key

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[ C ]

Solution

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A great circle can always be drawn through any two distinct points on the surface of the sphere.

Say the marksman will hit the points P₁, P₂, and P₃. Draw a great circle through P₁ and P₂ dividing the sphere into two hemispheres. Since P₁ and P₂ are on the boundary of these hemispheres, they belong to both hemispheres. Now P₃ can be on any of the two hemispheres. Hence, the three points will always be on the same hemisphere.

Probability, P = 1.0 answer [ C ]