Some more Probability.

\(A\) is an archer whose probability of killing a target he aims at is \(\frac{1}{3}\). He wants to kill his enemy \(B\) who arrives at a park everyday between \(5\) pmto \(6\) pm and waits there for \(30 \) mins from his time of arrival. Archer \(A\) stays at the park for \(10 \) mins from his time of arrival (also between \(5\) pm and \(6\) pm). The probability that \(B\) is killed between \(5\) pm to \(6\) pm is given by \(\frac{a}{b}\) where \(a\) and \(b\) are co-prime. What is the value of \(a+b\) if \(A\) has only one shot?

Details: For \(B\) to get killed, both \(A\) and \(B\) must be present at the park at the same time and the \(A\)'s arrow must hit \(B\).

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