JEE Advance 2025 Paper 1

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. If $P(U) = \frac{1}{2}, P(V) = \frac{1}{10}$  , and $P(W) = \frac{1}{12}$  , then $P(T)$   is equal to