Probability — practice question

Rod $AB$, with non-uniform density, has length $0.6\text{ m}$ and weight $9\text{ N}$. Its centre of mass lies $0.4\text{ m}$ from $A$. End $A$ of the rod is touching a rough vertical wall. The rod is in equilibrium, perpendicular to the wall, because a light string is fixed to $B$. The string is at an angle of $30^\circ$ to the horizontal. The tension in the string is $T\text{ N}$ (see diagram).