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  4. In a convex hexagon two diagonals are drawn at random. The probability that the diagonals intersect at an interior point of the hexagon, is

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Q. In a convex hexagon two diagonals are drawn at random. The probability that the diagonals intersect at an interior point of the hexagon, is

Probability

Solution:

$n(S)=$ total number of selections of two diagonals
$={ }^{9} C_{2}=\frac{9 \times 8}{2}=36$
$n(E)=$ the number of selections of two diagonals which intersect at an interior point $=$ the total number of selections of four vertices $={ }^{6} C_{4}=15$
$\therefore $ The required probability $=\frac{15}{36}=\frac{5}{12}$.