Spinning Spherical Target: Probability for Three Marksmen to Hit on the Same Hemisphere

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 ]