Find the probability that none of the three bulbs in a set of traffic lights will have to be replaced during the first 1200 hours of operation if the lifetime X of a bulb (in thousands of hours) is a random variable with probability density function f(x) = 6[0.25 – (x – 1.5)²] when 1 < x < 2 and f(x) = 0 otherwise. You should assume that the lifetimes of different bulbs are independent.

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