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 ​8.2% 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?.
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?