The computing system at a large university is currently undergoing shutdown for
ID: 3202467 • Letter: T
Question
The computing system at a large university is currently undergoing shutdown for repairs. Previous shutdowns have been due to hardware failure, software failure, or power (electronic failure. The system is forced to shutdown 73% of the time when it experiences hardware problems, 12% of the time when it experiences software problem, and 88% of the time when it experiences electronic problem. Maintenance engineers have determined that probabilities of hardware, software, and power problems are .01, .05, and .02 respectively. What is the probability that the current shutdown is due to hardware failure? Software problem? Power failure?Explanation / Answer
P(hardware problem) = 0.01
P(software problem) = 0.05
P(power problem) = 0.02
P(shutdown | hardware problem) = 0.73
P(shutdown | software problem) = 0.12
P(shutdown | power problem) = 0.88
P(shutdown) = P(shutdown | hardware problem) * P(hardware problem) + P(shutdown | software problem) * P(software problem) + P(shutdown | power problem) * P(power problem)
= 0.73 * 0.01 + 0.12 * 0.05 + 0.88 * 0.02
= 0.0309
a) P(shutdown due to hardware failure) = P(shutdown | hardware problem) * P(hardware problem) / P(shutdown)
= 0.73 * 0.01 / 0.0309
= 0.24
b) P(shutdown due to software failure) = P(shutdown | software problem) * P(software problem) / P(shutdown)
= 0.12 * 0.05 / 0.0309
= 0.19
c) P(shutdown due to power failure) = P(shutdown | power problem) * P(power problem) / P(shutdown)
= 0.88 * 0.02 / 0.0309
= 0.57
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