When a certain biased die is rolled, a particular face occurs with...

Probability of obtaining total sum $7 =$

Probability of getting opposite faces.

Probability of getting opposite faces

$= 2\left[\left(\dfrac{1}{6} - x\right)\left(\dfrac{1}{6} + x\right) + \dfrac{1}{6} \times \dfrac{1}{6} + \dfrac{1}{6} \times \dfrac{1}{6}\right] = 2\left[\left(\dfrac{1}{6} - x\right)\left(\dfrac{1}{6} + x\right) + \dfrac{1}{6} \times \dfrac{1}{6} + \dfrac{1}{6} \times \dfrac{1}{6}\right] = \dfrac{13}{96}$

$x = \dfrac{1}{8}$