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?
Answer
(A)
Explanation
In one roll, a 6 comes with probability \(\frac{1}{6}\) and any other face with probability \(\frac{5}{6}\), and the three rolls are independent. The single 6 can be on the first, second or third roll, so \(P = 3 \times \frac{1}{6} \times \left(\frac{5}{6}\right)^2 = 3 \times \frac{25}{216} = \frac{75}{216}\).
Answer: A