You have to distinguish two things:
-existence of emergency situation (0.002)
-probability that the alarm will respond to the emergency situation (0.98)
Hence, alarm sounds when rare emg. situation exists: 0.98*0.002=0.00196
There is a possibility that the emergency situation exists and that the alarm fails to respond (1-0.98).
This is like when a building that has an alarm, and one day a thief breaks in. The alarm may and may not sound.
There is also a probability that the alarm sounds and that the emergency situation does not exist. Like when a vibration from a truck trigers the alarm.
alarm sounds when rare emg. situation doesn`t exist: 0,01*0,998=0.00998
Therefore, when the alarm sounds, it may or may not be an emergency situation. These two events are independent and we have to add their probability.0.00196+0.00998=0.01194
The question is what is the probability that emergency situation trigered the alarm, if the alarm already sounds.
We have to divide probability of the emergency trigered alarm to the added probability of emergency and non-emergency trigered alarm, which represents any case when the alarm sounds.
So, the ans is 0.00196/0.01194=0.164
HTH