nick1816 wrote:
Number of ways you can select 2 verices= 8C2=28
Number of ways these vertices form a diagonal= (1/2)*(8C1 * 1)=4
the probability that these vertices form a diagonal of the octagon. = 4/28=1/7
A diagonal of a polygon is any line connecting two vertices that is not an edge, so an octagon has quite a few diagonals -- I think you're only counting lines connecting vertices that are strictly opposite each other.
Here we can select a pair of vertices in 8*7/2! = 28 ways. If we draw a line between our pair of vertices, it will be a diagonal unless it's one of the 8 edges of the octagon. So we can draw 28 - 8 = 20 diagonals, and the answer is 20/28 = 5/7.
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