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# emergency

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A chemical plant has an emergency alarm system. When an emergency situation exists, the alarm sounds with probability 0.95. When an emergency situation does not exist, the alarm sounds with probability 0.02. A real emergency situation is a rare event, with probability 0.004. Given that the alarm has just sounded, what is the probability that a real emergency situation exists

Feb 18, 2020

$$P[\text{emergency|alarm}] = \\ \dfrac{P[\text{alarm|emergency}]P[\text{emergency}]}{P[\text{alarm}]} = \\ \dfrac{0.95 \cdot 0.004}{0.95\cdot 0.004 + 0.02 \cdot 0.996} = 0.160202$$