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 7.5% 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 if the 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 total malfunction would not be impossible, but it would be unlikely. No, because total malfunction would still not be unlikely. 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.

Explanation / Answer

the probability of failure = 0.075

therefore probability of non failure = 0.925

a) the probability that th exam clock will not work = probability of failure of clok = 0.075

b) the probability that 2 clock fails = 0.075^2 = 0.075*0.075 = 0.0056

c)the student will not awake only when all the three clock fails

therefore probability that he 3 clcok fails = 0.075^3 = 0.00042

d) as we have seen that the probability of failing 2 clock or 3 clock is less then the probability of failing one clock therefore the reliability has increase. therefore option A is correct.

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