# Some more Probability.

Discrete Mathematics Level 4

$$A$$ 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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