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?

Select one answerSingle correct

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Solution

Step-by-step verified solution

Official answer: A) (75)/(216)

Quantitative Aptitude

This problem can be modeled using the Binomial Probability Distribution:

P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}

Here:

Number of trials, $n = 3$
Number of successful outcomes ('6'), $k = 1$
Probability of rolling a '6' in a single roll, $p = \frac{1}{6}$
Probability of not rolling a '6' in a single roll, $q = 1 - p = \frac{5}{6}$

Substitute these values into the formula:

P(X = 1) = \binom{3}{1} \left(\frac{1}{6}\right)^1 \left(\frac{5}{6}\right)^{3-1}

P(X = 1) = 3 \times \frac{1}{6} \times \frac{25}{36} = \frac{75}{216}

Thus, the correct option is (A).

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This Quantitative Aptitude previous year question is Q8 of the GATE CSE 2025 Set 1 paper. Find more GATE CSE PYQs on Quantitative Aptitude in General Aptitude, or browse all GATE CSE PYQs.

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Quantitative Aptitude in GATE CSE

Quantitative Aptitude has 53 GATE CSE PYQs across 13 papers from 2011 to 2026. 27 of them are 2-mark MCQs like this one, and GATE CSE 2025 Set 1 has 4.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.