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 11.7​% 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?   nothing ​(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?   nothing ​(Round to five decimal places as​ needed.) c. What is the probability of not being awakened if the student uses three independent alarm​ clocks?   nothing ​(Round to five decimal places as​ needed.) d. Do the second and third alarm clocks result in greatly improved​ reliability?     A. ​Yes, because total malfunction would not be​ impossible, but it would be unlikely.   B. ​No, because the malfunction of both is equally or more likely than the malfunction of one.   C. ​No, because total malfunction would still not be unlikely.   D. ​Yes, because you can always be certain that at least one alarm clock will work.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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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
11.7​%
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?
 
nothing
​(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?
 
nothing
​(Round to five decimal places as​ needed.)
c. What is the probability of not being awakened if the student uses three independent alarm​ clocks?
 
nothing
​(Round to five decimal places as​ needed.)
d. Do the second and third alarm clocks result in greatly improved​ reliability?
 
 
A.
​Yes, because total malfunction would not be​ impossible, but it would be unlikely.
 
B.
​No, because the malfunction of both is equally or more likely than the malfunction of one.
 
C.
​No, because total malfunction would still not be unlikely.
 
D.
​Yes, because you can always be certain that at least one alarm clock will work.
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