A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight identical components, each with a probability of 0.3 of failing in less than 1,000 hours. The sub system will operate if any four of the eight components are operating. Assume that the components operate independently. (Round your answers to four decimal places.) (a) Find the probability that exactly four of the eight components last longer than 1,000 hours. (b) Find the probability that the subsystem operates longer than 1,000 hours.

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Chapter1: Combinatorial Analysis
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A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight identical components, each with a probability of 0.3 of failing in less than 1,000 hours. The sub system will operate if any four of the eight components are
operating. Assume that the components operate independently. (Round your answers to four decimal places.)
(a) Find the probability that exactly four of the eight components last longer than 1,000 hours.
(b) Find the probability that the subsystem operates longer than 1,000 hours.
Transcribed Image Text:A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight identical components, each with a probability of 0.3 of failing in less than 1,000 hours. The sub system will operate if any four of the eight components are operating. Assume that the components operate independently. (Round your answers to four decimal places.) (a) Find the probability that exactly four of the eight components last longer than 1,000 hours. (b) Find the probability that the subsystem operates longer than 1,000 hours.
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