SOLUTION: Two of the vertices of a regular octahedron are to be chosen at random. What is the probability that they will be the endpoints of an edge of the octahedron? Express your answer as

Question 1189311: Two of the vertices of a regular octahedron are to be chosen at random. What is the probability that they will be the endpoints of an edge of the octahedron? Express your answer as a common fraction.
Answer by greenestamps(13208) (Show Source): You can put this solution on YOUR website!

A regular octahedron (picture two square pyramids attached base to base) has 6 vertices and 12 edges.

The number of ways of choosing 2 of the 6 vertices is

ANSWER: The probability that 2 vertices chosen randomly on an octahedron are the endpoints of an edge of the octahedron is 12/15 = 4/5

That answer might seem surprising, but it is easily seen to be correct if you have a good picture of the octahedron as being two square pyramids joined base to base. The only pairs of vertices of the octahedron that do NOT form an edge are the two pairs of opposite corners of the square bases and the "peaks" of the two pyramids.

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