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 18.5​% 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 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.

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 5.6​% 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?     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?     c. What is the probability of not being awakened if the student uses three independent alarm​ clocks?     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. ​No, because total malfunction would still not be unlikely.   C. ​Yes, because total malfunction would not be​ impossible, but it would be unlikely.   D. ​Yes, because you can always be certain that at…

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A certain tennis player makes a successful first serve 78​% of the time. Assume that each serve is independent of the others. If she serves 9​times, what's the probability she gets​: Part 1 ​a) The probability that she gets all 9 serves in is _______________ ​(Round to three decimal places as ​needed.). Part 2 ​b) The probability she gets exactly 4 serves in is _______________ ​(Round to three decimal places as​ needed.) Part 3 ​c) The probability she gets at least 7 serves in is ______________________ ​(Round to three decimal places as​ needed.) Part 4 ​d) The probability that there are no more than 6 serves in is __________ ​(Round to three decimal places as​ needed.)