2. Intrusion Detection: (25 points) The servers at Cornell's data center are partitioned into three groups labeled A, B, and C. The notorious hacker P. Vladimir has established a backdoor in one of the servers in Group C. The Cornell IT expert C. Ezra aims to identify the compromised server. Not knowing which group the compromised server belongs to, he randomly chooses, with equal probability, a group to examine. If he chooses Group A to examine, it will take him one day to complete and not finding the compromised server (since there is none in this group). If he chooses Group B to examine, it will take him two days to complete and not finding the compromised server (again since there is none in this group). If he chooses Group C to examine, it will take him three days to complete and successfully identify the compromised server. Suppose that each time after completing the examination of a group and not finding the compromised server, he will again randomly choose, with equal probability, a group to examine. The amount of time it takes him to complete examining a group is the same as given above, no matter how many times he