Question

Three of the six vertices of a regular hexagon are chosen at random. The probability that triangle formed by these vertices is equilateral is

• A. $\frac{1}{20}$
• B. $\frac{1}{10}$
• C. $\frac{1}{5}$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$\frac{1}{10}$

AEC and DBF are equilateral triangles

$P\left(E\right)=\frac{2}{{}^2{C}_3}=\frac{2}{20}=\frac{1}{10}$