A system consists of two identical pumps, #1 and #2. If one pump fails, the system will still operate. However, because of the added strain, the remaining pump is now more likely to fail than was originally the case. That is, ?r ?= ?P?(#2 fails ??#1 fails) > ?P?(#2 fails) = ?q. ?If at least one pump fails by the end of the pump design life in 7% of all systems and both pumps fail during that period in only 1%, what is the probability that pump #1 will fail during the pump design life?

Answer: Step 1 of 1 Let A be the event that Pump #1 fails and B be the event that Pump #2 fails. We are given that: P(at least one pump fails) = 0.07 P(A or B) = 0.07 P(both pumps fail) = 0.01 P(A and B) = 0.01 Since both pumps are identical, we can assume that P(A) = P(B). Recall the following...