An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5,…
2026
An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice in succession and the number on the top face is recorded each time. The probability that the number appearing in the second roll is an integer multiple of the number appearing in the first roll is __________
- A.
1/6
- B.
5/18
- C.
7/18
- D.
5/6
Attempted by 6 students.
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Correct answer: C
For each first roll a, count the possible second rolls b such that b is an integer multiple of a.
If a = 1, b can be 1, 2, 3, 4, 5, 6: 6 outcomes.
If a = 2, b can be 2, 4, 6: 3 outcomes.
If a = 3, b can be 3, 6: 2 outcomes.
If a = 4, 5, or 6, only b = a works: 1 outcome each.
Total favorable ordered pairs = 6 + 3 + 2 + 1 + 1 + 1 = 14.
Total possible ordered pairs = 6 × 6 = 36.
Therefore, the required probability is 14/36 = 7/18.
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