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 18.7 ​% 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. ​No, because the malfunction of both is equally or more likely than the malfunction of one. B. ​Yes, because you can always be certain that at least one alarm clock will work. C. ​No, because total malfunction would still not be unlikely. D. ​Yes, because total malfunction would not be​ impossible, but it would be unlikely. Click to select your answer(s

Answer 1

a) It is given that the probability that an alarm clock will not work is 0.187. so our required probability of the alarm clock not working on the morning of an important final exam is 0.187

b. Probability of two alarm clocks not working = 0.187*0.187= 0.03497

c. Probability of three alarm clocks not working= 0.187*0.187*0.187= 0.00654

d. Yes, as we can see that the probability of 2/3 alarm clocks not working is lesser than the probability of 1 alarm clock not working. The total malfunction here is not impossible but it is very unlikely. So option D is correct.