The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a teacher’s alarm clock has a 0.975 probability of working on any given morning.
(a) Find the probability that the teacher’s alarm clock will not work on the morning of the lecture. (3 marks)
(b) If the teacher has two such alarm clocks, find the probability that they both fail on the morning of an important lecture.
(3 marks)
(c) If the teacher has two such alarm clocks, find the probability the teacher is being awakened by the alarm clock. A person typically needs at least one functional alarm to wake up.
(4 marks)