Dfinity promises its customers that network services are 90% reliability. The network consists of three serial nodes, each of which must work for the network to be operational. Consistent with its customer guarantee, the reliability of each node is 90%; however, the company has been receiving complaints about its service.

a. Calculate the reliability of the network. Are customer complaints justified?

b. Dfinity is considering adding nodes to its network structure so that each of the current nodes is “backed up” by a lesser node with a reliability of 80%. What is the reliability of this revised network?