Two fair dice are thrown. The numbers on them are taken as λ and μ,...

\left|\begin{cases}1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & \lambda\end{cases}\right| = \lambda - 5

{\Delta}_{1} = \left|\begin{cases}1 & 1 & 5 \\ 2 & 3 & \mu \\ 3 & \lambda & 1\end{cases}\right| = 10\lambda + 3\mu - \lambda \mu - 44

{\Delta}_{2} = \left|\begin{cases}1 & 1 & 5 \\ 1 & 3 & \mu \\ 1 & \lambda & 1\end{cases}\right| = 5\lambda + \mu - \lambda \mu - 13

{\Delta}_{3} = \left|\begin{cases}1 & 1 & 5 \\ 1 & 2 & \mu \\ 1 & 3 & 1\end{cases}\right| = - 2\mu + 6

For unique solution
$\lambda \ne 5, \mu \in { 1, 2, 3, 4, 5, 6 }$

$⇒ p = \dfrac{5}{6} \times 1 = \dfrac{5}{6}$
For No Solution
$\lambda = 5, \mu \ne 3$

$⇒ q = \dfrac{1}{6} \times \dfrac{5}{6} = \dfrac{5}{36}$