in n sided regular hexagon find the probability that the two diagonals chosen at random will intersect inside the polygon.?
in a hexagon , number of sides = 6
the number of diagonals =
now the number of ways of choosing any 2 diagonals =
now since the diagonals intersect inside the polygon, let us choose any 4 points out of 6 vertices,
so that they will form a quadrilateral and the diagonals of a quadrilateral must intersect inside it.
thus the total number of ways such that diagonals will intersect inside the hexagon =
thus the required probability = 15/36 = 5/12
hope this helps you
the number of diagonals =
now the number of ways of choosing any 2 diagonals =
now since the diagonals intersect inside the polygon, let us choose any 4 points out of 6 vertices,
so that they will form a quadrilateral and the diagonals of a quadrilateral must intersect inside it.
thus the total number of ways such that diagonals will intersect inside the hexagon =
thus the required probability = 15/36 = 5/12
hope this helps you