The optimal scheduling of preventive maintenance tests of some (but not all) of n independently operating components was developed in Reliability Engineering and System Safety (January 2006). The time (in hours) between failures of a component was approximated by an exponential distribution with mean θ. Suppose θ = 1000 hours. Given that the time between failures is at least 1,500 hours, what is the probability that the time between failures is less than 2,000 hours?

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