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 9.1% daily failure rate. Complete parts (a) through (d) below.
a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? Round to 3 decimal points.
b. 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 5 decimal places.
c. What is the probability of not being awakened if the student uses three independent alarm clocks? Round to 5 decimal places.
d. Do the second and third alarm clocks result in greatly improved reliability?
A. No, because total malfunction would still not be unlikely.
B. No, because the malfunction of both is equally or more likely than the malfunction of one.
C. Yes, because total malfunction would not be impossible, but it would be unlikely.
D. Yes, because you can always be certain that at least one alarm clock will work.

Explanation / Answer

a) P(Clock will fail) = 0.091

b) P(Both clocks will fail) = 0.0912 = 0.00828

c) P(All three will fail) = 0.0913 = 0.00075

d) Option C is correct.

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