Two identical printers are used in ITO for printing. The life of the printers follows an exponential distribution. The mean time between failures is 1000 hours. Please answer the following questions.

a) What is the probability that a printer will fail within 800 hours?

b) What is the probability that a printer will fail within 800-1000 hours?

c) Suppose both printers are bought brand new at the beginning of the fall semester. The fall semester lasts for 1000 hours. What is the probability that only 1 printer is working by the end of the fall semester? (Suppose broken printers will not be replaced or repaired until the spring semester)