Question

Question Help 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 6.7% 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? (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

Answer 1

(a)  

Alarm clocks that fail at 6.7% on a day

   =6.7% (given)

=0.067

(b) The probability that both alarm clocks will fail is 0.067²

=0.067*0.067

=0.004489

=0.00449

(c) The probability of failure of three independent alarm clock will be 0.067³

=0.067*0.067*0.067

=0.00030

(d) Second and third alarm clocks result greatly improved reliability,

Ans : Yes,because total malfunction would not be impossible ,but it would be unlikely

since the probability of failure has been reduced from 0.067 to 0.00030

and sucess rate inceresing (1-0.067)% =93.3% to (1-0.0003) %=99.97%