In the communication network given below, link failures are independent, and each link has a probability of failure p. (consider the physical situation). A can communicate with B as long as they are connected by at least one path which contains only in-service links.
Given that exactly five links have failed, determine the probability that A can still communicate with B.
Given that exactly five links have failed, determine the probability that either g or h (but not both) is still operating properly.
Given that a, d, and h have failed (and no other information), determine the probability that A can communicate with B.