Question: Redundancy in Alarm Clock: A statistics professor wants to ensure that she is not late for an early class because of a malfunctioning alarm clock. Instead of using one alarm clock, she decides to use three.

(a) What is the probability that at least one of her alarm clocks works correctly if each individual alarm clock has a 95% chance of working correctly?

(b) Does the professor really gain much by using three alarm clocks instead of only one?