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 ___________

Let $(x, y)$ denote the outcome of the two rolls, where $x$ is the number on the first roll and $y$ is the number on the second roll.

The total number of possible outcomes when rolling a six-faced die twice is:

We need to find the number of favorable outcomes where $y$ is an integer multiple of $x$ ($y = kx$ for some positive integer $k$):

• For $x = 1$: $y \in \{1, 2, 3, 4, 5, 6\} \implies 6$ outcomes

• For $x = 2$: $y \in \{2, 4, 6\} \implies 3$ outcomes

• For $x = 3$: $y \in \{3, 6\} \implies 2$ outcomes

• For $x = 4$: $y \in \{4\} \implies 1$ outcome

• For $x = 5$: $y \in \{5\} \implies 1$ outcome

• For $x = 6$: $y \in \{6\} \implies 1$ outcome

Total number of favorable outcomes:

Therefore, the required probability is:

Hence, the correct option is C.