The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that your alarm clock has a 0.9 probability of working on any given morning.

a. What is the probability that your alarm clock will not work on the morning of an important final exam?

b. If you have two such alarm clocks, what is the probability that they both fail on the morning of an important final exam?

c.With one alarm clock, you have a 0.9 probability of being awakened. What is the probability of being awakened if you use two alarm clocks?

d. Does a second alarm clock result in greatly improved reliability?