A chemical plant has an emergency alarm system. When an emergency situation exists, the alarm sounds with a probability of 0.95.

When an emergency situation does not exist, the alarm sounds with a probability of 0.02. A real emergency situation is a rare event, with a probability 0.004. Given that the alarm has just sounded, what is the probability that a real emergency situation exists?

When an emergency situation does not exist, the alarm sounds with a probability of 0.02. A real emergency situation is a rare event, with a probability 0.004. Given that the alarm has just sounded, what is the probability that a real emergency situation exists?