A chemical plant has an emergency alarm system for given batch reaction. When an

Question

A chemical plant has an emergency alarm system for given batch reaction. When an emergency situation exists, the alarm sounds with probability 90%. When an emergency does not exist, the alarm system sounds with probability 5%. Based on investigations and records, an emergency situation with the batch reaction is a rare event ; it has probability of 0.4%. Answer (a)-(c).

a)What is the probability that the alarm sounds for a batch reaction? a. 0.0040 b. 0.0335 C. 0.0534 d. 0.1046 e. 0.0004

b) Given that the alarm has just sounded, what is the probability that an emergency situation exists? A. 0.067 b.0.5020 c. 1601 d.0.0225 e. 0.0004

c) Given that the alarm has not sounded, what is the probability that an emergency situation exists?

Explanation / Answer

Ans:

a)

P(alarm sounds)=0.9*0.004+0.05*(1-0.004)=0.0534

Option C is correct.

b)P(emergency exist/alarm sounded)=P(alarm sound/emerency exist)*P(emergency exists)/P(alarm sounds)

=(0.9*0.004)/0.0534=0.067

Option A is correct.

c)P(alarm not sounds)=1-0.0534=0.947

P(alarm does not sound/emerency exist)=1-0.9=0.1

P(emergency exist/alarm not sounded)=P(alarm does not sound/emerency exist)*P(emergency exists)/P(alarm does not sounds)

=(0.1*0.004)/0.947=0.0004

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