Experience shows that the failure rate of a certain electrical component is a linear function. Suppose that after two full days of operation, the failure rate is 10% per hour and after three full days of operation, it is 15% per hour.
(a) Find the probability that the component operates for at least 30 hours.
(b) Suppose that the component has been operating for 30 hours. What is the probability that it fails within the next hour?