JEE PYQ: Probability Question 37
Question 37 - 2019 (12 Apr Shift 1)
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:
(1) $\frac{1}{10}$
(2) $\frac{1}{5}$
(3) $\frac{3}{10}$
(4) $\frac{3}{20}$
Show Answer
Answer: (1)
Solution
Total triangles $= {}^6C_3 = 20$. Equilateral triangles in regular hexagon $= 2$ (alternate vertices). $P = \frac{2}{20} = \frac{1}{10}$.
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