Given Figure shows the connectivity diagram of a computer network that connects node A to node B along different possible paths. The labeled branches of the diagram display the probabilities for which the links in the network are up;
for example, 0.8 is the probability that the link from node A to intermediate node C is up, and so on for the other links. Link failures in the network are assumed to be independent of each other.
a. When all the links in the network are up, find the probability that there is a path connecting node A to node B.
b. What is the probability of complete failure in the network, with no connection from node A to node B?
