2. Probability estimation

(a) A taxicab was involved in a fatal hit-and-run accident at night, two cab companies, the Green and the Blue, operate in the city. You are told that: (i) 75% of the cabs in the city are Green and 25% are blue; (ii) a witness identified the cab as blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness was correct in identifying the color of the cab 80% of the time. What is the probability that the cab involved in the accident was really Blue?

(b) Similar to (a), we continue our false alarm rate estimation, the likelihood of a malicious attack is 0.01%, 99.5% of the time, the IDS recognizes a malicious event as malicious. 0.05% of the time, the IDS issues an alarm when the event is benign. What is the false alarm rate now?