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  • Please help! Three vertices of a regular hexagon are chosen at random . The probability that the triangle with these three vertices is not equilateral equals

Three vertices of a regular hexagon are chosen at random . The probability that the triangle with these three vertices is not equilateral equals

  • Option 1)

    \frac{1}{10}

  • Option 2)

    \frac{9}{10}

  • Option 3)

    \frac{1}{2}

  • Option 4)

    \frac{3}{4}

 

Answers (1)

best_answer

Total number or triangles are 

6_{C_{3}}=\frac{6!}{3!\: 3!}

\frac{6\times 5\times 4}{6}

=20

in which only equilateral triangle will be formed

\therefore \frac{2}{20}=\frac{1}{10}

Proability of Triangles which are not equilateral 

Triangle is  1-\frac{1}{10} =\frac{9}{10}


Option 1)

\frac{1}{10}

Option is incorrect

Option 2)

\frac{9}{10}

Option is correct

Option 3)

\frac{1}{2}

Option is incorrect

Option 4)

\frac{3}{4}

Option is incorrect

Posted by

Aadil

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