A system has n independent units, each of which falls with probability p. The system fails only if k or more units fail. What is the Probability that the system fails? Solution probability of failure = p probabaility of sucess=1-p System has n independent units. probability that system fails= probability that k units fail +probability that k+1 units fail .....+probability that n units fail = pk(1-p)n-k+pk+1(1-p)n-k-1+....+pn-1(1-p)+pn.