In order to improve the reliability of a critical control loop, it is proposed that redundant sensors be used. Suppose that three independent sensors are employed and each sensor works properly 95% of the time.
(a) What is the probability that all three sensors are functioning properly?
(b) What is the probability that none of the sensors are functioning properly?
(c) It is proposed that the average of the three measurements be used for feedback control. Briefly critique this strategy.