(a) A lamp has two bulbs, each of a type with average lifetime 1,200 hours. Assuming that we can model the probability of failure of a bulb by an exponential density function with mean = 1,200, find the probability that both of the lamp's bulbs fail within 1,200 hours. (Round your answer to four decimal places.) (b) Another lamp has just one bulb the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1,200 hours. (Round your answer to four decimal places.)

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