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GATE CSE 2025 Session 1 Q8: Probability of exactly one six in three rolls

Question

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?

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Answer: A (official GATE 2025 final answer key)

Concept used: Binomial probability: choose which roll is the six.

First step: P=(31)⋅16⋅(56)2P = \binom{3}{1} \cdot \dfrac{1}{6} \cdot \left(\dfrac{5}{6}\right)^2.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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