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GATE 2025 CS (CS1) – Question 8

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 2 marks · Multiple choice

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?

  1. $\frac{75}{216}$
  2. $\frac{1}{6}$
  3. $\frac{1}{18}$
  4. $\frac{25}{216}$

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Correct answer: (A) $\frac{75}{216}$

Explanation

P = C(3,1)(1/6)(5/6)^2 = 3*25/216 = 75/216.