Two fair dice are thrown. The numbers on them are taken as \(\lambda\) and \(\mu\), and a system of linear equations \(x…

Two fair dice are thrown. The numbers on them are taken as \(\lambda\) and \(\mu\), and a system of linear equations \(x+y+z=5\), \(x+2 y+3 z=\mu\) and \(x+3 y+\lambda z=1\) is constructed. If \(p\) is the probability that the system has a unique solution \(q\) is the probability that the system has no solution, then

[JEE Main 2021, 26 Aug (Shift 2)]