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?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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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?

Expert Solution
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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