Probability

Let $0 < x < \frac{1}{6}$ be a real number. When a certain biased dice is rolled, a particular face $F$ occurs with a probability $\frac{1}{6} - x$ and its opposite face occurs with a probability $\frac{1}{6} + x$ ; the other four faces occur with probability $\frac{1}{6}$ . Recall that the opposite faces sum to $7$ in any dice. Assume that the probability of obtaining the sum $7$ when two such dice are rolled is $\frac{13}{96}$ . Then the value of $x$ is :