Now suppose the service provided using distributed computing requires only 1 of the 3 computers, with the other 2 computer being backups (that is, each of the three computers, on its own, is capable of providing the service). Now what is the probability that the service will not be available at any time, assuming that no other components in the distributed system will fail? How does it compare with the failure probability if the same computing is performed using monolithic computing, that is, on one computer only?

In this exercise we will use a simplified mathematical model to analyze failures in a distributed system. Explain your answers.
Suppose each computer in has a probability of p of failing at any time.

The failure probability is pn in general, or (0.2)3 = 0.008 in this case.
Because only any one of the three computers needs to be up for the service to be available, the failure probability is now less than when exactly one single computer is needed.