Discussion
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 ___
Answer: C
The probability is \(\frac{7}{18}\).
There are 36 equally likely ordered pairs (first, second). Count the pairs where the second number is a multiple of the first:
- first 1: 1, 2, 3, 4, 5, 6 (6 pairs)
- first 2: 2, 4, 6 (3 pairs)
- first 3: 3, 6 (2 pairs)
- first 4, 5 or 6: only itself (1 pair each, 3 in all)
\[ P = \frac{6+3+2+3}{36} = \frac{14}{36} = \frac{7}{18} \]
1/6 counts only the six pairs where both rolls match, and 5/18 also undercounts; 5/6 is far too large, since a large first roll such as 4, 5 or 6 allows only one second roll.
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