Question

the principle of redundancy is used when system reliability is improved through redundant or backup components. assume that a students alarm clock has a 10.7% daily failure rate. complete parts (a) through (d) below.
a. what is the probability that the students alarm clock will not work on the morning of an important final exam?
0.107 (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.)

Explanation:

Step1: Identify failure rate of one clock

The daily failure rate of one alarm - clock is $p = 0.107$.

Step2: Use multiplication rule for independent events

Since the failures of the two alarm - clocks are independent events, the probability that both fail is the product of their individual failure probabilities. If the probability of the first clock failing is $p_1$ and the probability of the second clock failing is $p_2$, and $p_1=p_2 = 0.107$, then the probability that both fail is $P=p_1\times p_2$.
$P = 0.107\times0.107=0.01145$

Answer:

$0.01145$