ion list 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 $17.1 \%$ daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? 0.171 (Round to three decimal places as needed.) 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? (Round to five decimal places as needed.)

Step 1 ：Given that the daily failure rate of the student's alarm clock is 17.1% or 0.171.

Step 2 ：The probability that the student's alarm clock will not work on the morning of an important final exam is 0.171.

Step 3 ：If the student has two such alarm clocks, the probability that they both fail on the morning of an important final exam is the probability of one alarm clock failing multiplied by the probability of the second alarm clock failing.

Step 4 ：Since the two events are independent (the failure of one does not affect the failure of the other), we can simply multiply the probabilities together.

Step 5 ：\(prob\_single\_failure = 0.171\)

Step 6 ：\(prob\_both\_fail = prob\_single\_failure \times prob\_single\_failure = 0.029241\)

Step 7 ：Final Answer: The probability that both alarm clocks fail on the morning of an important final exam is approximately \(\boxed{0.02924}\).