Three students $S_1, S_2,$ and $S_3$ are given a problem to solve. Consider the following events:

U: At least one of $S_1, S_2,$ and $S_3$ can solve the problem,

V: $S_1$ can solve the problem, given that neither $S_2$ nor $S_3$ can solve the problem,

W: $S_2$ can solve the problem and $S_3$ cannot solve the problem,

T: $S_3$ can solve the problem.

For any event $E$, let $P(E)$ denote the probability of $E$. If

$P(U) = \dfrac{1}{2}$ , $P(V) = \dfrac{1}{10}$ , and $P(W) = \dfrac{1}{12}$,

then $P(T)$ is equal to