A fair six-faced dice, with the faces labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and…
2025
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?
- A.
\(75 \over {216}\) - B.
\(1 \over {6}\) - C.
\(1 \over {18}\) - D.
\(25 \over {216}\)
Attempted by 65 students.
Show answer & explanation
Correct answer: A
Correct probability:
Use the binomial reasoning. Exactly one '6' in three rolls means choose which one of the three rolls is the six, and the other two must not be six.
Number of ways to choose the roll that shows 6: 3
Probability for a specific chosen pattern (one fixed position is 6 and the other two are not): (1/6) * (5/6) * (5/6) = 25/216
Multiply by the 3 possible positions: 3 * 25/216 = 75/216 = 25/72 ≈ 0.3472
Therefore the probability of rolling '6' exactly once in three rolls is 75/216, which simplifies to 25/72.
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