The principle of redundancy is used when system reliability is improved through

Question

The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 7.4% daily failure rate. Complete parts (a) through (d) below. What is the probability that the student's alarm clock will not work on the morning of an important final exam? Round to three decimal places as needed.) If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? (Round to five decimal places as needed.) What is the probability of not being awakened he student uses three independent alarm clocks? (Round to five decimal places as needed.) Do the second and third alarm clocks result in greatly improved reliability? Yes, because you can always be certain that at least one alarm clock will work. No because the malfunction of both is equally or more likely than the malfunction of one. No because total malfunction would still not be unlikely. Yes, because total malfunction would not be impossible, but it would be unlikely.

Explanation / Answer

a)

Probablity of alaram does not work(failure) = 0.074

b)

Probability of 2 independent alaram does not work = 0.074*0.074 = 0.5475%

c)

Probability of 3 independent alaram does not work = 0.074*0.074*0.074 = 0.0405%

d)

You can see how the probability of failure (student does not wake) decreases as no of independent alarams increases.

Yes, because you can always be certain that at least one alaram will work

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