A large aircraft manufacturer produces a passenger jet having a navigation component consisting of three sequentially functioning redundant navigation systems that will allow the jet to be properly controlled so long as at least one of the systems remain operational. The operating life of each of the systems is the outcome of a random variable having the exponential PDF \(f(x)=\) \(.1 e^{-.1 x} I_{(0, \infty)}(x)\) where \(x\) is measured in 1,000 's of hours and the operating lives are independent of one another.

(a) What is the probability that the navigation component will continue to function for at least 20,000 hours?

(b) In an economizing mode, a redesign of the jet is being considered that will reduce the navigation component from three redundant systems to two. How does this affect the probability of the event in \((\mathrm{a})\) ?