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:
