Discuss the below:
The local area network (LAN) for the faculty of engineering computing system at the University of Waterloo is temporary shut down for repairs. Previous shut downs have been due to hardware failure, software failure or power failure. Maintenance engineers have determined that the probabilities of hardware, software and power problems are 0.01, 0.05, 0.02, respectively. They have also determined that if the system experiences hardware problems, it shuts down 73% of the time. Similarly, if software problems occur, the system shuts down 12% of the time; and if power failure occurs, the system shuts down 88% of the time. What is the probability that the current shut down of the LAN is due to hardware failure.