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Question: 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 system sounds with probability 0.02. A real emergency situation is a rare event with probability 0.04.

[A]     Given that the alarm just sounded, what is the probability that a real emergency situation does not exist?
[B]    Given that the alarm did not sound, what is the probability that a real emergency situation exists? What is the probability that an emergency does not exist and the alarm does not sound?
[C]     Find the probability that the alarm will not sound given that an emergency situation exists?
[D]     Find the probability that an alarm will sound?

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