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Three types of customers arrive at a service station. The times required to service type 1...

Three types of customers arrive at a service station. The times required to service type 1 and type 2 customers are exponential random variables with respective means 1 and 10 seconds. Type 3 customers require a constant service time of 2 seconds. Suppose that the proportion of type 1, 2 and 3 customers is 1/2, 1/8 and 3/8, respectively. Find the probability that an arbitrary customer requires more than 15 seconds of service time.

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