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  • In a convex hexagon two diagonals are drawn at random. The probability that the diagonals intersect at an interior point of the hexagon isOption: 1 <

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

Option: 1

\frac{5}{12}


Option: 2

\frac{7}{12}


Option: 3

\frac{2}{5}


Option: 4

None of these 


Answers (1)

best_answer

\mathrm{n(S)=} Total number of sections of two diagonals

\mathrm{={ }^6 C_2-6 C_2={ }^9 C_2=\frac{9 \times 8}{2}=36} .
\mathrm{n(E)=} The number of selections of two diagonals which intersect at an interior point
= The number of selections of four vertices \mathrm{={ }^6 C_4=15} .

\therefore  The required probability =\frac{15}{36}=\frac{5}{12} .
 

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Rishi

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