Dasholytics Inc runs an online analytics dashboard. The company employs three machines-Server $1,$ Server $2,$ and Server $3$ - to serve the data for the dashboard. At any point in time one of these three machines has the job of serving the data, and the other two are kept in standby mode. Dasholytics uses a server scheduler (software) that decides which of the three machines should serve the data at any given point of time. The scheduler switches between data servers without disrupting the data feed to the dashboard.
The machine which is serving the data sometimes fails to do so; in this case an alert is sent out to the Dasholytics team and they investigate and fix the problem. The time for which a machine fails to serve data is accounted as service outage caused by that machine. For technical reasons the server scheduler is deactivated when there is such an outage; the outage gets over only when the issue with the server is fixed and it is put back online.
The figures below describe the server usage and outage statistics as compiled over the last one year ( $365$ days). Please use this information to answer the questions that follow.
Figure $1:$ Figure (a) shows the total service outage caused by each server, as a percentage of the total time that it served data. Figure (b) shows the total time that each server served data, as a percentage of the total duration over which this information was collected.
As part of their due diligence, a potential customer of Dasholytics picks a random point in time during the year and checks the status of the dashboard. What is the probability that the customer finds that there was a service outage at this point in time, and that Server $1$ was the server responsible for serving data at that time?
