Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to

$\frac{1}{10}$

Total number of triangles which can be formed $= {^6C}_3 =\frac{6×5×4}{1×2×3}=20$

Number of equilateral triangles = 2.

∴ Required probability $=\frac{2}{20}=\frac{1}{10}.$