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Probability of Lamp Failure

A lamp has two bulbs, each of a type with an average lifetime of 6 hours. The probability density function for the lifetime of a bulb is f(t) =(1/6) e^(-t/6), t <= 0.
What is the probability that both of the bulbs will fail within 3 hours?

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Probability of Lamp Failure is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.