The Center for High Assurance Computer Systems at the Naval Research Laboratory in Washington, D.C. has developed several theoretical models for detecting intruder attacks on high-consequence computer systems (International Information Assurance Workshop, March 2005). Consider a naive attacker against a computer system with two servers. Server A will detect the intruder with probability .95. Server B detects the intruder with probability .99.

a. If the two servers operate in series, find the probability that the intruder is detected.

b. If the two servers operate in parallel, find the probability that the intruder is detected.

c. Suppose the system is designed so that only one of the two servers is operating at a time. Server A is in operation 1/3 of the time, and Server B is in operation 2/3 of the time. Find the probability that the system will detect the naive intruder.