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?
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)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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
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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