Question

Three of the six vertices of a regular hexagon are chosen at random. What is the probability that the triangle with these vertices is equilateral?

Options

• `3/10`

• `3/20`

• `1/20`

• `1/10`

Answer 1

`1/10`

Explanation:

ABCDEF is a regular hexagon.

Total number of triangles ⁶C₃ = 20. ....(Since no three points are collinear).

Of these only ∆ACE; ∆BDF are equilateral triangles.

Therefore, required probability = `2/20 = 1/10`.