There is a pyramid with equilateral base and it is placed on a circle of infinite radius. The centre of the triangle and the circle coincide. What is the probability(or what it tends to) that we select a point on the circle and be able to see two faces of the pyramid.
2026-04-06 07:34:57.1775460897
probability question involving infinite space
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The lines extending the sides of the triangle partition the plane into a bounded region (the triangle) and six unbounded regions: three adjacent to the sides, and three adjacent to the vertices. To see a pair of sides you need to be in a region adjacent to a vertex. Each of these is V-shaped with angle $\frac{\pi}{3}$. Therefore at infinity they make up approximately half the circle, hence the probability is one half.