A website server runs continuously (24 hours a day, 7 days a week) . Support personnel are only available between 8:00 am and 5:00 pm (7 days a week). If a server goes down it can be easily reset, however if this downtime occurs during off-hours the website will remain down until support starts again the next morning. The server has a MTBF of 1,200 hours and has been running for 30 days as of 8:00 am Monday morning. What is the probability that the website will still be operational come 8:00 am Wednesday morning?
If you were to use the exponential probability function would the first 720 hours that the system has been running even matter since we know that it didn't fail during that time?