GATE CS 2025 Set 1 — Question 8
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Engineering Mathematics → Probability & Statistics → Discrete Distributions
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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?
Correct answer
(A) (75)/(216)
Solution
This is a binomial probability problem with trials.
The probability of success (rolling a '6') in a single trial is .
The probability of failure (not rolling a '6') is .
We want to find the probability of exactly success in trials.
Using the binomial formula :
.
The probability of success (rolling a '6') in a single trial is .
The probability of failure (not rolling a '6') is .
We want to find the probability of exactly success in trials.
Using the binomial formula :
.
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