This problem demonstrates the concept of redundancy, the principle of improving reliability of systems by using redundant or backup components. Suppose a hydraulic system on an airplane has a 5% probability of failing. a) What is the probability that the hydraulic system does not fail (that is, the flight is completed safely)?
b) Now, suppose that the airplane has three independent hydraulic systems that each have a 5% probability of failure. What is the probability that all three systems fail?
c) Supposing that the airplane will safely complete its flight if at least one of the three independent hydraulic systems is functioning, what is the probability that the airplane will safely complete its flight?
d) What effect does having a redundancy of three independent hydraulic systems have on the probability of a safe flight?