A computer network consists of 3 servers. The operating times (in years) of server-1 and of server-2 are uniform random variables with respective parameters (0, 3) and (0, 4). The operating times of server-1 and server-2 are independent from each other and are also independent from the operating time of server-3. However, operating time of server-3 depends on the operating times of servers 1 and 2. If at least one of server-1 and server-2 break down before 2 years, operating time of server-3 is Uniform on (0,5), otherwise it is Uniform on (0, 6).
a. What is the probability that the operating time of server-3 is more than 2 years?
b. The network is said to be robust if at least one of the three servers operate more than 2 years. What is the probability that the network is robust?
c. If it is known that the network is robust, what is the probability that the operating time of server-3 is more than 2 years?