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Probability : Exponential Density Function

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a) A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can model the probbility of failure of these bulbs by an exponential density function with mean mu = 1000. Find the probability that both of the bulbs fail in 1000 hours.
b) Another lamp has one bulb of the same type. If it burns out , it is replaced with another. Find the probability that both fail within a total of 1000 hours.

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Probabilities are calculated using an exponential density function with step-by-step details provided.

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