Island public service ltd has an emergency alarm system at its power station in old harbour bay. When an emergency situation exist the alarm sounds with probability .95 When an emergency situation does not exist, the alarm sounds with probability .2 A real situation emergency situation is a rare event, with probability .004 Given that the alarm has just sounded, what is the probability that a real emergency situation exists?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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 Island public service ltd has an emergency alarm system at its power station in old harbour bay. When an emergency situation exist the alarm sounds with probability .95 When an emergency situation does not exist, the alarm sounds with probability .2 A real situation emergency situation is a rare event, with probability .004 Given that the alarm has just sounded, what is the probability that a real emergency situation exists?

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Step 1

From the given information,

Consider,

E is the event that shows real emergency exists.

EC is the event that shows real emergency does not exist.

A be the event that show the alarm sounds.

P (E) = 0.004

P (EC) = 1-0.004

         = 0.996

P (A|E) =0.95

P (A| EC) = 0.2

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