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Two light bulbs are installed at the same time, and each was taken from a batch of bulbs with an expected lifetime of 1000 hours (so the time until each one burns out is exponentially distributed with μ = 1000). Whether one burns out is independent of when the other one burns out.
(a) What is the probability that both bulbs will still be working after 1200 hours?
(b) What is the probability that both bulbs will have burned out before 1200 hours?
Report answers in decimal places.
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