(Solution) - A component has an exponential failure time distribution with a -(2025 Original AI-Free Solution)

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A component has an exponential failure time distribution with a mean time to failure of 35 days.
(a) What is the probability that the component is still operating after 35 days?
(b) What is the probability that the component fails within 40 days?
(c) If six of these components are placed in series, what is the probability that the system is still operating after 5 days?