A computer server relies on the following independent components: • Two identical…
MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
A computer server relies on the following independent components:
• Two identical power supply units (PSUs) wired in parallel, each working with probability 0.92.
• A cooling fan that must work; its probability of working is 0.95.
• A processor module that must work; its probability of working is 0.97.
Additionally, if both PSUs fail simultaneously, an automatic backup generator starts with probability 0.90 and supplies power in place of the failed PSUs. The server operates successfully if it receives power (either from at least one PSU or from the backup generator) and both the fan and the processor are working.
(i) Show that the probability that at least one of the two PSUs supplies power is 1−(0.08)2.
(ii) Find the probability that the server operates when at least one PSU supplies power.
(iii) Determine the probability that the server operates solely through the backup generator route (both PSUs fail but the generator starts).
(iv) Hence, calculate the overall probability that the server operates successfully.