A student appears for tests I, II and III. The student is considered successful if he passes in tests I, II or I, III or all the three. The probabilities of the Student passing in tests II and III are m, n and $\frac{1}{2}$ respectively. If the probability of the student to be successful is $\frac{1}{2}$, then which one of the following is correct? (a) $m\left(1+n\right)=1$ (B) $n\left(1+m\right)=1$ (C) $m=1$ (D) $mn=1$

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