Probability Question 60
Question: 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
[IIT 1995; MP PET 2002, 04]
Options:
A) $ \frac{1}{2} $
B) $ \frac{1}{5} $
C) $ \frac{1}{10} $
D) $ \frac{1}{20} $
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Answer:
Correct Answer: C
Solution:
Total number of triangles which can be formed is equal to $ {}^{6}C_3=\frac{6\times 5\times 4}{1\times 2\times 3}=20 $
Number of equilateral triangles = 2
$ \therefore $ Required probability $ =\frac{2}{20}=\frac{1}{10}. $
BETA
