JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Probability

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If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is:

(A) $\frac{3}{10}$
(B) $\frac{1}{5}$
(C) $\frac{1}{10}$ ✓ Correct
(D) $\frac{3}{20}$

Answer: (C)

Solution

A regular hexagon has

6

vertices, so three of them can be chosen in

(3 6) = 20

ways. An equilateral triangle is formed only by taking alternate vertices, and there are exactly two such triangles,

A_{1} A_{3} A_{5}

and

A_{2} A_{4} A_{6}

. The probability is therefore

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

JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Single correct option

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