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.