Suppose that the waiting time to see the doctor at a clinic is exponentially distributed with mean 50 minutes. The consultation time with the doctor is uniformly distributed between 10 and 20 minutes. If both these variables are independent, what is the probability that the total time spent at the clinic is less than one hour?

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Suppose that the waiting time to see the doctor at a clinic is exponentially distributed with mean 50 minutes. The consultation time with the doctor is uniformly distributed between 10 and 20 minutes. If both these variables are independent, what is the probability that the total time spent at the clinic is less than one hour?
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