Gate CS 2025 (CS1)| Question - 8 | General Aptitude

April 04, 2025

A fair six-faced dice, with the faces labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, is rolled thrice. What is the probability of rolling ‘6’ exactly once?

$\frac{75}{216}$

$\frac{1}{6}$

$\frac{1}{18}$

$\frac{25}{216}$

Solution:

Let X represent number of '6' when the dice is rolled thrice. Clearly X is a Binomial random with parameters n =3 and P = $\frac{1}{6}$

$P (X = 1) = 3 C ₁ (\frac{1}{6})^{1}, {\frac{5}{6}}^{3 - 1} = 75 / 216$

general aptitude GA

Gate CS 2025 (CS1)| Question - 8 | General Aptitude

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