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.

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.