Question: A machine consists of two components: A and B. The machine needs both components to operate. As soon as one component breaks the machine fails.

A machine consists of two components: A and B. The machine needs both components to operate. As soon as one component breaks the machine fails. The time until component A breaks is an exponential with rate _A = 0.1 per year. The time until component B breaks is an exponential with rate _B = 0.4 per year. The two components are independent. Compute the probability the machine fails within the next 3 years.

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