Each of us must sometimes wake up early for something really important, such as a final exam, job interview, or an early flight. Assume that a battery-powered alarm clock has a 0.005 probability of failure, a smartphone alarm clock has a 0.052 probability of failure, and an electric alarm clock has a 0.001 probability of failure.

a. What is the probability that your single battery-powered alarm clock works successfully when you need it?

b. If you use a battery-powered alarm clock and a smartphone alarm clock, what is the probability that they both fail? What is the probability that both of them do not fail?

c. If you use a battery-powered alarm clock and a smartphone alarm clock and an electric alarm clock, what is the probability that they all fail? What is the probability that they don’t all fail? Express both of these answers using eight decimal places.

d. What configuration gives you the best chance to wake up for something really important?