Fix your company’s crashed system. You know that there are three possible source

Question

Fix your company’s crashed system. You know that there are three possible sources of errors in the system: the disk drive, the memory and the operating system.

Historical data: 50% of the errors are disk errors, 30% are memory errors and the remaining errors are operating system errors.

From component performance standards, you know that when a disk error occurs, the probability that the computer crashes is 60%, when a memory error occurs, the probability that the computer crashes is 70%, and when an operating system error occurs, the probability that the computer crashes is 40%.

The company computer has just crashed! You need to quickly decide which component (disk drive, memory or operating system) is the best component to look at first in your attempt to get the computer back on line.

Calculate all of the relevant conditional probabilities. Then, using this information, which component should you probably investigate first?

Explanation / Answer

Let

A = Disk error

B = Memory error

C = Operating system error

D = computer crashes

P(A) = 0.50

P(B) = 0.30

P(C)= 0.20

P(D/A) = 0.60

P(D/B) = 0.70

P(D/C) = 0.40

By Multiplication Theorem:
P(DA) = P(D/A) P(A) = 0.60 X 0.50 = 0.30

P(DB) = P(D/B) P(B) = 0.70 X 0.30 = 0.21

P(DC) = P(D/C) P(C) = 0.40 X 0.20 = 0.08

We note that among the 3possibilities, the probability of computer crashes and disk error occurs = 0.30 is the maximum.

So, disk component should be investigated first.

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