A pump system depends on a single power supply and three pumps (one powerful pump and two less powerful pumps). The system functions normally using the power supply and the powerful pump. If the powerful pump fails, the system still functions if the power supply and the two less powerful pumps are operational. If the power supply fails, a manual operator can operate any one of the three pumps so that the system functions. Use the following notation: A: power supply B: powerful pump C: less powerful pump D: less powerful pump O: operator The probabilities of component failure (per year) are as follows: PIA) = 0.001 P(B)= 0.01 P(C)=P(D) 0.005 P(O)=0.002 a. Draw a function block diagram of the pump system. b. Draw a fault tree of the pump system. C. What is the probability of the system failing? (use minimum cut sets) d. Let E represent the event of a power outage, where P(E)=0.01. If a power outage were to occur, what is the probability of failure of A? e. Assume that, given a power outage event, the probability of failure of all pumps increases by a factor of 50 (e. g., P(BE)=50*P(B)), while the operator will still deliver a reliable service. Assuming that the probability of failure given no event are identical to the unconditional probabilities, how much would the probability of system failure be?