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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?

 Dec 31, 2018

Best Answer 

 #1
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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.

 Dec 31, 2018
 #1
avatar+27329 
+3
Best Answer

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.

Alan Dec 31, 2018

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