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 19.1% 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 three decimal places as​ needed.) 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 five decimal places as​ needed.) c. What is the probability of not being awakened if the student uses three independent alarm​ clocks? -​(Round to five decimal places as​ needed.)

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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 19.1% 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 three decimal places as​ needed.)

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 five decimal places as​ needed.)

c. What is the probability of not being awakened if the student uses three independent alarm​ clocks? -​(Round to five decimal places as​ needed.)

 

d. Do the second and third alarm clocks result in greatly improved​ reliability?
A.​Yes, because you can always be certain that at least one alarm clock will work.
 
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.​No, because total malfunction would still not be unlikely.
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