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 6.8% daily failure rate.

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 total malfunction would still not be unlikely.
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.
Yes, because you can always be certain that at least one alarm clock will work.

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AlonsoDehner AlonsoDehner · Answer 1 · 2018-10-22T11:22:07+02:00

Answer:

Step-by-step explanation:

let X be the random variable for number of times the clock fails .

X is Poisson with average = 6.8% = 0.0068

PDF of x = e^(-0.0068) 0.0068^x/x!

a) The probability that the student's alarm clock will not work on the morning of an important final exam = P(X=0) = 0.00675

b) If the student has two such alarm clocks, the probability that they both fail on the morning of an important final exam:

Since both clocks are independent prob for both failing is

P(x1 fails) *P(x2 fails) = 0.00675(0.00675) = 0.000455625

c) the probability of not being awakened if the student uses three independent alarm clocks = Prob for all 3 fails = 0.00675^3

= 0.00000307546

d) Yes. Because all three fail probability is almost zero.

D. Yes, because you can always be certain that at least one alarm clock will work.