i need help on both these problems plz 8. The computing system at a large univer

Question

i need help on both these problems plz

8. The computing system at a large university has been forced to shut down 73% of the time when it periences hardware problems, 12% of the time when it experiences software problems, and 8% of the time when it experiences power problems. Maintenance engineers have determined that the probabilities of ardware, software, and power problems are .01,.05, and.02 respectively a) What is the probability of the system experiencing a power problem and being forced to shut down? (b) What is the probability of the system being shut down? 43 Probability Systew (c) What is the probability that if the sysem has shut down, it was due to a power failure.? was due 51.

Explanation / Answer

8:

Let H shows th event of hardware problem, P shows the event of software problem and S shows the event of software problems. So we have

P(H) = 0.01, P(S) = 0.05, P(P) = 0.02

Let F shows the event of force shutdown. So,

P(F|H) = 0.73, P(F|S) = 0.12, P(F|P) = 0.08

a)

The required probability is

P(F and P) = P(F|P) P(P) = 0.08 * 0.02 = 0.0016

b)

The probability that system is being shutdown is

P(F) = P(F|P)P(P)+P(F|H)P(H)+P(F|S)P(S) = 0.0016 + 0.0073+0.006=0.0149

c)

P(P|F) = [P(F|P)P(P)] / P(F) = 0.0016 / 0.0149 = 0.1074

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