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 sum of the two recorded numbers is a prime number is $\_\_\_\_$ .

For positive real numbers $S$ and $K$, the function $H_K(S)$ is defined as: $H_K(S)=\max (S-K, 0)$. The max function is defined as:

$$ \max (a, b)= \begin{cases}a, & \text { when } a>b \\ b, & \text { when } a \leq b\end{cases} $$

The graph below shows the plot of a function $N(S)$ versus $S$. $N(S)$ can be expressed as $\_\_\_\_$ .

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 $\_\_\_\_$

Which one of the following options is correct for the given data in the table?