MCQ
When a certain biased die is rolled, a particular face occurs with probability $\frac{1}{6}-\mathrm{x}$ and its opposite face occurs with probability $\frac{1}{6}+\mathrm{x}$. All other faces occur with probability $\frac{1}{6}$. Note that opposite faces sum to $7$ in any die. If $0\,<\,x\,<\,\frac{1}{6}$, and the probability of obtaining total $\mathrm{sum}=7$, when such a die is rolled twice, is $\frac{13}{96}$, then the value of $x$ is:
- A$\frac{1}{16}$
- B$\frac{1}{8}$
- C$\frac{1}{9}$
- D$\frac{1}{12}$