Modern manufacturing techniques rely on highly reliable components. Because of the difficulty and time to test the separate components of a computer system, for example, these are often completely assembled before the power is ever applied. Assume that the computer fails to work properly if any component fails.
(a) Suppose that the rate of defects for each component of the system is only 0.1%. If the system is assembled out of 100 components, what is the probability that the assembled computer works when switched on, assuming the components are independent?
(b) For the probability that the system works to be 99%, what is the largest allowable defect rate for the components? Assume independence.
(c) Use Boole's inequality to estimate the probability that the system described in part (a) works. Why does Boole's inequality work so well in this example?