Suppose that a certain system contains three components which function independently of each other and which are connected in series, as defined in iExercise 4 of Sec. 3.7. so that the system fails as soon as one of the components fails. Suppose that the length of life of the first component, measured in hours, has an exponential distribution with parameter f3 = 0.00] ; the length of life of the second component has an exponential distribution with parameter fJ - 0.003; and the length of life of the third component has an exponential distribution with parameter P = 0.006. Determine the probability that the system will not fail before 100 hours.