A regular dodecahedron is a convex polyhedron with 12 regular pentagonal faces and 20 vertices. If two distinct vertices are chosen at random, what is the probability that the line connecting them lies inside the dodecahedron?
Having chosen the first vertex at random there are 9 others that can be reached from it with a line along a surface. Hence there are 19 - 9 = 10 others for which the line must go inside the dodecahedron. The probability is therefore 10/19.
Having chosen the first vertex at random there are 9 others that can be reached from it with a line along a surface. Hence there are 19 - 9 = 10 others for which the line must go inside the dodecahedron. The probability is therefore 10/19.
